How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem - SSAT Upper Level: Quantitative

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Question

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

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Answer

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

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Question

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Tap to reveal answer

Answer

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

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Question

Give the perimeter of the above parallelogram if .

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Answer

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\cdot \frac{\sqrt{3}}{3}= 24 \cdot \frac{\sqrt{3}}{3}= 8\sqrt{3}$ , and

$BC = AD = 2\cdot AB = 2 \cdot 8\sqrt{3} = 16 \sqrt{3}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 8\sqrt{3}+ 8\sqrt{3}+ 16\sqrt{3}+16\sqrt{3} = 48\sqrt{3}$

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Question

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Tap to reveal answer

Answer

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

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Question

Find the length of the hypotenuse in the right triangle below.

Tap to reveal answer

Answer

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

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Question

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Tap to reveal answer

Answer

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of .

← Didn't Know|Knew It →

Question

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Tap to reveal answer

Answer

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

← Didn't Know|Knew It →

Question

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Tap to reveal answer

Answer

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

← Didn't Know|Knew It →

Question

Give the perimeter of the above parallelogram if .

Tap to reveal answer

Answer

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\cdot \frac{\sqrt{3}}{3}= 24 \cdot \frac{\sqrt{3}}{3}= 8\sqrt{3}$ , and

$BC = AD = 2\cdot AB = 2 \cdot 8\sqrt{3} = 16 \sqrt{3}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 8\sqrt{3}+ 8\sqrt{3}+ 16\sqrt{3}+16\sqrt{3} = 48\sqrt{3}$

← Didn't Know|Knew It →

Question

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Tap to reveal answer

Answer

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

← Didn't Know|Knew It →

Question

Find the length of the hypotenuse in the right triangle below.

Tap to reveal answer

Answer

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

← Didn't Know|Knew It →

Question

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Tap to reveal answer

Answer

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of .

← Didn't Know|Knew It →

Question

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Tap to reveal answer

Answer

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

← Didn't Know|Knew It →

Question

Give the perimeter of the above parallelogram if .

Tap to reveal answer

Answer

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\cdot \frac{\sqrt{3}}{3}= 24 \cdot \frac{\sqrt{3}}{3}= 8\sqrt{3}$ , and

$BC = AD = 2\cdot AB = 2 \cdot 8\sqrt{3} = 16 \sqrt{3}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 8\sqrt{3}+ 8\sqrt{3}+ 16\sqrt{3}+16\sqrt{3} = 48\sqrt{3}$

← Didn't Know|Knew It →

Question

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Tap to reveal answer

Answer

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

← Didn't Know|Knew It →

Question

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Tap to reveal answer

Answer

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

← Didn't Know|Knew It →

Question

Find the length of the hypotenuse in the right triangle below.

Tap to reveal answer

Answer

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

← Didn't Know|Knew It →

Question

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Tap to reveal answer

Answer

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of .

← Didn't Know|Knew It →

Question

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Tap to reveal answer

Answer

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

← Didn't Know|Knew It →

Question

Give the perimeter of the above parallelogram if .

Tap to reveal answer

Answer

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\cdot \frac{\sqrt{3}}{3}= 24 \cdot \frac{\sqrt{3}}{3}= 8\sqrt{3}$ , and

$BC = AD = 2\cdot AB = 2 \cdot 8\sqrt{3} = 16 \sqrt{3}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 8\sqrt{3}+ 8\sqrt{3}+ 16\sqrt{3}+16\sqrt{3} = 48\sqrt{3}$

← Didn't Know|Knew It →

Knew It

How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem - SSAT Upper Level: Quantitative

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Use the Pythagorean Theorem to find the length of the hypotenuse.

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

You need to use the Pythagorean Theorem, which is . Add the first two values and you get . Take the square root of both sides and you get .

Give the perimeter of the above parallelogram if .

By the Theorem: , and The perimeter of the parallelogram is

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Using the numbers given to us by the question, units

Find the length of the hypotenuse in the right triangle below.

Use the Pythagorean Theorem to find the hypotenuse.

If James traveled north and John traveled west from the same town, how many miles away will they be from each other when they reach their destinations?

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Use the Pythagorean Theorem to find the length of the hypotenuse.

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

You need to use the Pythagorean Theorem, which is . Add the first two values and you get . Take the square root of both sides and you get .

Give the perimeter of the above parallelogram if .

By the Theorem: , and The perimeter of the parallelogram is

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Using the numbers given to us by the question, units

Find the length of the hypotenuse in the right triangle below.

Use the Pythagorean Theorem to find the hypotenuse.

If James traveled north and John traveled west from the same town, how many miles away will they be from each other when they reach their destinations?

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

You need to use the Pythagorean Theorem, which is . Add the first two values and you get . Take the square root of both sides and you get .

Give the perimeter of the above parallelogram if .

By the Theorem: , and The perimeter of the parallelogram is

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Using the numbers given to us by the question, units

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Use the Pythagorean Theorem to find the length of the hypotenuse.

Find the length of the hypotenuse in the right triangle below.

Use the Pythagorean Theorem to find the hypotenuse.

If James traveled north and John traveled west from the same town, how many miles away will they be from each other when they reach their destinations?

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

You need to use the Pythagorean Theorem, which is . Add the first two values and you get . Take the square root of both sides and you get .

Give the perimeter of the above parallelogram if .

By the Theorem: , and The perimeter of the parallelogram is

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}:cm$

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .