Rectangles - Math
Card 1 of 180
George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 
and costs $40. One quart of paint covers 100 
and costs $15. How much money will he spend on the blue paint?
George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400
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The area of the walls is given by 
One gallon of paint covers 400 
and the remaining 140 
would be covered by two quarts.
So one gallon and two quarts of paint would cost 
The area of the walls is given by
One gallon of paint covers 400
So one gallon and two quarts of paint would cost
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If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?
If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?
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Area of a rectangle is = lw
Perimeter = 2(l+w)
We are given 34 = 2(l+w) or 17 = (l+w)
possible combinations of l + w
are 1+16, 2+15, 3+14, 4+13... ect
We are also given the area of the rectangle is 52 meters squared.
Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52
Therefore the longest side of the rectangle is 13 meters
Area of a rectangle is = lw
Perimeter = 2(l+w)
We are given 34 = 2(l+w) or 17 = (l+w)
possible combinations of l + w
are 1+16, 2+15, 3+14, 4+13... ect
We are also given the area of the rectangle is 52 meters squared.
Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52
Therefore the longest side of the rectangle is 13 meters
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Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?
Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?
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Leaving the width to be x, the length is 4_x_. The total perimeter is 4_x_ + 4_x_ + x + x = 10x.
We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.
Leaving the width to be x, the length is 4_x_. The total perimeter is 4_x_ + 4_x_ + x + x = 10x.
We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.
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A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
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Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
P = 2_w_ + 2_l_ = 2(2_x_) + 2(3_x_ + 5) = 4_x_ + 6_x_ + 10 = 10_x_ + 10 = 10(x + 1)
Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
P = 2_w_ + 2_l_ = 2(2_x_) + 2(3_x_ + 5) = 4_x_ + 6_x_ + 10 = 10_x_ + 10 = 10(x + 1)
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If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
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the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
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The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?
The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?
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Glass Area per Window = 8 ft x 6 ft = 48 ft2
Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows
Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft2
Glass Area per Window = 8 ft x 6 ft = 48 ft2
Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows
Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft2
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If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?
If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?
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96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.
96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.
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The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?
The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?
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The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in2.
The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in2.
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Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
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Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
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Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
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Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x = 
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x =
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
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Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
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We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
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A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?
A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?
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We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)
We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)
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A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
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The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
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Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
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First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
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If the area Rectangle A is 
larger than Rectangle B and the sides of Rectangle A are 
and 
, what is the area of Rectangle B?
If the area Rectangle A is
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The rectangular bathroom floor in Michael’s house is ten feet by twelve feet. He wants to purchase square tiles that are four inches long and four inches wide to cover the bathroom floor. If each square tile costs $2.50, how much money will Michael need to spend in order to purchase enough tiles to cover his entire bathroom floor?
The rectangular bathroom floor in Michael’s house is ten feet by twelve feet. He wants to purchase square tiles that are four inches long and four inches wide to cover the bathroom floor. If each square tile costs $2.50, how much money will Michael need to spend in order to purchase enough tiles to cover his entire bathroom floor?
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The dimensions for the bathroom are given in feet, but the dimensions of the tiles are given in inches; therefore, we need to convert the dimensions of the bathroom from feet to inches, because we can’t compare measurements easily unless we are using the same type of units.
Because there are twelve inches in a foot, we need to multiply the number of feet by twelve to convert from feet to inches.
10 feet = 10 x 12 inches = 120 inches
12 feet = 12 x 12 inches = 144 inches
This means that the bathroom floor is 120 inches by 144 inches. The area of Michael’s bathroom is therefore 120 x 144 in2 = 17280 in2.
Now, we need to find the area of the tiles in square inches and calculate how many tiles it would take to cover 17280 in2.
Each tile is 4 in by 4 in, so the area of each tile is 4 x 4 in2, or 16 in2.
If there are 17280 in2 to be covered, and each tile is 16 in2, then the number of tiles we need is 17280 ÷ 16, which is 1080 tiles.
The question ultimately asks us for the cost of all these tiles; therefore, we need to multiply 1080 by 2.50, which is the price of each tile.
The total cost = 1080 x 2.50 dollars = 2700 dollars.
The answer is $2700.
The dimensions for the bathroom are given in feet, but the dimensions of the tiles are given in inches; therefore, we need to convert the dimensions of the bathroom from feet to inches, because we can’t compare measurements easily unless we are using the same type of units.
Because there are twelve inches in a foot, we need to multiply the number of feet by twelve to convert from feet to inches.
10 feet = 10 x 12 inches = 120 inches
12 feet = 12 x 12 inches = 144 inches
This means that the bathroom floor is 120 inches by 144 inches. The area of Michael’s bathroom is therefore 120 x 144 in2 = 17280 in2.
Now, we need to find the area of the tiles in square inches and calculate how many tiles it would take to cover 17280 in2.
Each tile is 4 in by 4 in, so the area of each tile is 4 x 4 in2, or 16 in2.
If there are 17280 in2 to be covered, and each tile is 16 in2, then the number of tiles we need is 17280 ÷ 16, which is 1080 tiles.
The question ultimately asks us for the cost of all these tiles; therefore, we need to multiply 1080 by 2.50, which is the price of each tile.
The total cost = 1080 x 2.50 dollars = 2700 dollars.
The answer is $2700.
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Ron has a fixed length of wire that he uses to make a lot. On Monday, he uses the wire to make a rectangular lot. On Tuesday, he uses the same length of wire to form a square-shaped lot. Ron notices that the square lot has slightly more area, and he determines that the difference between the areas of the two lots is sixteen square units. What is the positive difference, in units, between the length and the width of the lot on Monday?
Ron has a fixed length of wire that he uses to make a lot. On Monday, he uses the wire to make a rectangular lot. On Tuesday, he uses the same length of wire to form a square-shaped lot. Ron notices that the square lot has slightly more area, and he determines that the difference between the areas of the two lots is sixteen square units. What is the positive difference, in units, between the length and the width of the lot on Monday?
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Let’s say that the rectangular lot on Monday has a length of l and a width of w. The area of a rectangular is the product of the length and the width, so we can write the area of the lot on Monday as lw.
Next, we need to find an expression for the area of the lot on Tuesday. We are told that the lot is in the shape of a square and that it uses the same length of wire. If the length of the wire used is the same on both days, then the perimeter will have to remain the same. In other words, the perimeter of the square will equal the perimeter of the rectangle. The perimeter of a rectangle is given by 2_l_ + 2_w_.
We also know that if s is the length of a side of a square, then the perimeter is 4_s_, because each side of the square is congruent. Let’s write an equation that sets the perimeter of the rectangle and the square equal.
2_l_ + 2_w_ = 4_s_
If we divide both sides by 4 and then simplify the expression, then we can write the length of the square as follows:
Let’s say that the rectangular lot on Monday has a length of l and a width of w. The area of a rectangular is the product of the length and the width, so we can write the area of the lot on Monday as lw.
Next, we need to find an expression for the area of the lot on Tuesday. We are told that the lot is in the shape of a square and that it uses the same length of wire. If the length of the wire used is the same on both days, then the perimeter will have to remain the same. In other words, the perimeter of the square will equal the perimeter of the rectangle. The perimeter of a rectangle is given by 2_l_ + 2_w_.
We also know that if s is the length of a side of a square, then the perimeter is 4_s_, because each side of the square is congruent. Let’s write an equation that sets the perimeter of the rectangle and the square equal.
2_l_ + 2_w_ = 4_s_
If we divide both sides by 4 and then simplify the expression, then we can write the length of the square as follows:
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A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the area of the rectangle?
A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the area of the rectangle?
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Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
A = lw = (3_x_ + 5)(2_x_) = 6_x_2 + 10_x_
Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
A = lw = (3_x_ + 5)(2_x_) = 6_x_2 + 10_x_
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Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – _x_2 , and points C and D lie on the graph of y = _x_2 – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?
Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – _x_2 , and points C and D lie on the graph of y = _x_2 – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?
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A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?
A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?
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Rectangle
B = 2_H_
B = 8”
H = B/2 = 8/2 = 4”
Area = B x H = 8” X 4” = 32 in2
Rectangle
B = 2_H_
B = 8”
H = B/2 = 8/2 = 4”
Area = B x H = 8” X 4” = 32 in2
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