How to find the length of the side of a square - ISEE Upper Level: Quantitative Reasoning
Card 1 of 28
Which is the greater quantity?
(a) The sidelength of a square with area 
square inches.
(b) The sidelength of a square with perimeter 
inches.
Which is the greater quantity?
(a) The sidelength of a square with area
(b) The sidelength of a square with perimeter
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 
square inches has sidelength 
inches.
(b) A square with perimeter 
inches has sidelength 
inches.
(a) is the greater quantity.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area
(b) A square with perimeter
(a) is the greater quantity.
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Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength 
inches.
(b) A square with perimeter 80 inches has sidelength 
inches.
The two quantities are equal.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength
(b) A square with perimeter 80 inches has sidelength
The two quantities are equal.
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The perimeter of a square is 
. Give the length of each side in terms of 
.
The perimeter of a square is
Tap to reveal answer
Divide the perimeter of a square by 4 to get its sidelength:
Divide the perimeter of a square by 4 to get its sidelength:
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The area of a square is 169 square inches. What is the length of one side (
in the diagram below)?
The area of a square is 169 square inches. What is the length of one side (
Tap to reveal answer
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side 
is a number that, when multiplied by itself is equal to 169.
In other words, take the square root of 169 to find the length of 
.
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side
In other words, take the square root of 169 to find the length of
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If the perimeter of a square is 36in, what is the length of one side?
If the perimeter of a square is 36in, what is the length of one side?
Tap to reveal answer
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
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Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Tap to reveal answer
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
← Didn't Know|Knew It →
A square has a perimeter of 60cm. Find the length of one side.
A square has a perimeter of 60cm. Find the length of one side.
Tap to reveal answer
A square has 4 equal sides. The formula to find perimeter of a square is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the square is 60cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the square is 15cm.
A square has 4 equal sides. The formula to find perimeter of a square is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the square is 60cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the square is 15cm.
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Which is the greater quantity?
(a) The sidelength of a square with area square inches.
(b) The sidelength of a square with perimeter inches.
Which is the greater quantity?
(a) The sidelength of a square with area
(b) The sidelength of a square with perimeter
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area square inches has sidelength inches.
(b) A square with perimeter inches has sidelength inches.
(a) is the greater quantity.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area
(b) A square with perimeter
(a) is the greater quantity.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength inches.
(b) A square with perimeter 80 inches has sidelength inches.
The two quantities are equal.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength
(b) A square with perimeter 80 inches has sidelength
The two quantities are equal.
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The perimeter of a square is . Give the length of each side in terms of .
The perimeter of a square is
Tap to reveal answer
Divide the perimeter of a square by 4 to get its sidelength:
Divide the perimeter of a square by 4 to get its sidelength:
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The area of a square is 169 square inches. What is the length of one side ( in the diagram below)?
The area of a square is 169 square inches. What is the length of one side (
Tap to reveal answer
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side is a number that, when multiplied by itself is equal to 169.
In other words, take the square root of 169 to find the length of .
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side
In other words, take the square root of 169 to find the length of
← Didn't Know|Knew It →
If the perimeter of a square is 36in, what is the length of one side?
If the perimeter of a square is 36in, what is the length of one side?
Tap to reveal answer
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
← Didn't Know|Knew It →
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Tap to reveal answer
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
← Didn't Know|Knew It →
A square has a perimeter of 60cm. Find the length of one side.
A square has a perimeter of 60cm. Find the length of one side.
Tap to reveal answer
A square has 4 equal sides. The formula to find perimeter of a square is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the square is 60cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the square is 15cm.
A square has 4 equal sides. The formula to find perimeter of a square is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the square is 60cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the square is 15cm.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The sidelength of a square with area square inches.
(b) The sidelength of a square with perimeter inches.
Which is the greater quantity?
(a) The sidelength of a square with area
(b) The sidelength of a square with perimeter
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area square inches has sidelength inches.
(b) A square with perimeter inches has sidelength inches.
(a) is the greater quantity.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area
(b) A square with perimeter
(a) is the greater quantity.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Which is the greater quantity?
(a) The sidelength of a square with area 400 square inches.
(b) The sidelength of a square with perimeter 80 inches.
Tap to reveal answer
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength inches.
(b) A square with perimeter 80 inches has sidelength inches.
The two quantities are equal.
The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:
(a) A square with area 400 square inches has sidelength
(b) A square with perimeter 80 inches has sidelength
The two quantities are equal.
← Didn't Know|Knew It →
The perimeter of a square is . Give the length of each side in terms of .
The perimeter of a square is
Tap to reveal answer
Divide the perimeter of a square by 4 to get its sidelength:
Divide the perimeter of a square by 4 to get its sidelength:
← Didn't Know|Knew It →
The area of a square is 169 square inches. What is the length of one side ( in the diagram below)?
The area of a square is 169 square inches. What is the length of one side (
Tap to reveal answer
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side is a number that, when multiplied by itself is equal to 169.
In other words, take the square root of 169 to find the length of .
Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side
In other words, take the square root of 169 to find the length of
← Didn't Know|Knew It →
If the perimeter of a square is 36in, what is the length of one side?
If the perimeter of a square is 36in, what is the length of one side?
Tap to reveal answer
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
To find the perimeter of a square, we will use the following formula:
where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of any side, we will solve for a.
Now, we know the perimeter of the square is 36in. So, we will substitute.
Therefore, the length of one side of the square is 9in.
← Didn't Know|Knew It →
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Tap to reveal answer
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the length of one side of her room?
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
← Didn't Know|Knew It →