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Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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Example Questions

Example Question #21 : 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 of the following right triangle.

Possible Answers:

$2\sqrt{29}$

$4\sqrt5$

$3\sqrt{21}$

$\sqrt{29}$

Correct answer:

$2\sqrt{29}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{10^2 + 4^2}=\sqrt{116}$

Simply:

$\sqrt{4}\cdot\sqrt{29}$

$2\sqrt{29}$

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Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$30\textup{ ft}$

$25\textup{ ft}$

$45\textup{ ft}$

$35\textup{ ft}$

$22\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

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Example Question #134 : Right Triangles

A right triangle has side lengths of 20 inches and 19 inches. What is the length of its hypotenuse?

Possible Answers:

H=36.6in

None of these.

H=42.6in

H=19in

H=27.6in

Correct answer:

H=27.6in

Explanation:

We can find any one missing side of a right triangle with the Pythagorean theorem.

a^2+b^2=c^2

19^2+20^2=c^2

361+400=c^2

Simplify and take the square root of both sides:

$\boldsymbol{c=27.6in}$

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Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 2

Given the right triangle above, find the length of the hypotenuse.

Possible Answers:

17.32

14.491

18.248

Correct answer:

18.248

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

a^2+b^2=c^2 .

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.

So, first we must square the values of the given sides of the triangle.

3^2=9

and

18^2=324 .

Next, we must add these two solutions to get 333 .

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal:

$\sqrt{333}\approx18.248$ .

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Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 1

Given the right triangle above, find the length of the hypotenuse.

Possible Answers:

5.477

15.553

19.643

21.26

Correct answer:

21.26

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

a^2+b^2=c^2 .

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.

So, first we must square the values of the given sides of the triangle.

14^2=196

and

16^2=256 .

Next, we must add these two solutions to get 452 .

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal:

$\sqrt{452}\approx21.26$ .

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Example Question #94 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 4

Find the length of the hypotenuse of the right triangle.

Possible Answers:

12.5

7.745

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

a^2+b^2=c^2 .

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.

So, first we must square the values of the given sides of the triangle.

5^2=25

and

12^2=144 .

Next, we must add these two solutions to get 169 .

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal:

$\sqrt{169}\approx13$ .

This example is another instance of a Pythagorean triple to keep in mind.

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Example Question #136 : Right Triangles

Tri 7

Find the length of the hypotenuse of the right triangle.

Possible Answers:

120

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

a^2+b^2=c^2 .

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.

So, first we must square the values of the given sides of the triangle.

15^2=225

and

8^2=64 .

Next, we must add these two solutions to get 289 .

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal:

$\sqrt{289}=17.$

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Example Question #95 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 10

Find the length of the hypotenuse of the right triangle.

Possible Answers:

43.829

37.21

70.81

Correct answer:

43.829

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

a^2+b^2=c^2 .

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.

So, first we must square the values of the given sides of the triangle.

25^2=625

and

36^2=1296 .

Next, we must add these two solutions to get 1921 .

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal:

$\sqrt{1921}\approx43.829$ .

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Example Question #92 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 12

Find the length of the hypotenuse of the above right triangle.

Possible Answers:

$\sqrt{14s^2}$

$\sqrt{53s}$

$\sqrt{18s^2}$

$\sqrt{49s^2}$

$\sqrt{53s^2}$

Correct answer:

$\sqrt{53s^2}$

Explanation:

Using the Pythagorean Theorem

a^2+b^2=c^2 ,

we can find the length of the hypotenuse in terms of variables.

First, square both given sides and add them together. Next, take the square root of that sum to find the length of the hypotenuse in terms of s.

The calculation should look like this:

$(7s)^2+(2s)^2=49s^2+4s^2=53s^2=\sqrt{53s^2}$

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Example Question #97 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the length of the hypotenuse of a right triangle whose other sides are 5cm and 12cm?

Possible Answers:

18cm

4.24cm

7cm

60cm

13cm

Correct answer:

13cm

Explanation:

Use Pythagorean Theorem

a^2+b^2=c^2

a and b are the sides of the triangle

(5)^2+(12)^2=c^2

c^2=169

c=13

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Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #21 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #134 : Right Triangles

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #94 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #136 : Right Triangles

Example Question #95 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #92 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #97 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

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