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

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Example Questions

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Possible Answers:

0.5

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

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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Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Parallelogram2

Give the perimeter of the above parallelogram if BD = 24 .

Possible Answers:

$48\sqrt{2}$

$24+24 \sqrt{2}$

$24+24 \sqrt{3}$

$32+16\sqrt{3}$

$48\sqrt{3}$

Correct answer:

$48\sqrt{3}$

Explanation:

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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Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Possible Answers:

units

4.64 units

5.20 units

5.38 units

Correct answer:

5.38 units

Explanation:

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

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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Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs with the lengths $4\:cm$ and $5\:cm$ . Find the length of the hypotenuse.

Possible Answers:

$41\:cm$

$3\:cm$

$\sqrt{35}\:cm$

$\sqrt{41}\:cm$

Correct answer:

$\sqrt{41}\:cm$

Explanation:

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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Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Possible Answers:

23.45

22.78

25.61

Correct answer:

25.61

Explanation:

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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Example Question #141 : Geometry

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?

Possible Answers:

$10\textup { miles}$

$60\textup { miles}$

$40\textup { miles}$

$30\textup { miles}$

$50\textup { miles}$

Correct answer:

$50\textup { miles}$

Explanation:

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 c=50 .

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

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #141 : Geometry

All SSAT Upper Level Math Resources

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