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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 Question #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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

Possible Answers:

$\sqrt{33}$

$\sqrt{34}$

$\sqrt{35}$

Correct answer:

$\sqrt{34}$

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.

$\text{Hypotenuse}=\sqrt{3^2 + 5^2}=\sqrt{34}$

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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:

$\sqrt{69}$

$\sqrt{66}$

$\sqrt{65}$

Correct answer:

$\sqrt{65}$

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.

$\text{Hypotenuse}=\sqrt{7^2 + 4^2}=\sqrt{65}$

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Example Question #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{14}$

$4\sqrt2$

$\sqrt{15}$

$3\sqrt3$

Correct answer:

$\sqrt{14}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(2\sqrt2)^2$

Simplify.

c^2=6+8

Solve.

c^2=14

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{14}$

Report an Error

Example Question #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{26}$

$6\sqrt2$

$4\sqrt5$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(\sqrt{19})^2$

Simplify.

c^2=6+19

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

Example Question #65 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt6$

$2\sqrt3$

$5\sqrt2$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{11})^2+(\sqrt{14})^2$

Simplify.

c^2=11+14

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

Example Question #66 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$3\sqrt3$

$4\sqrt2$

$\sqrt{26}$

Correct answer:

$\sqrt{26}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{10})^2+(4)^2$

Simplify.

c^2=10+16

Solve.

c^2=26

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{26}$

Report an Error

Example Question #62 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$8\sqrt3$

$6\sqrt5$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{10})^2+(\sqrt{39})^2$

Simplify.

c^2=10+39

Solve.

c^2=49

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{49}$

Simplify.

c=7

Report an Error

Example Question #63 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$16\sqrt2$

The length of the hypotenuse cannot be determined.

$4\sqrt6$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(2\sqrt{5})^2+(\sqrt{29})^2$

Simplify.

c^2=20+29

Solve.

c^2=49

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{49}$

Simplify.

c=7

Report an Error

Example Question #69 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt{14}$

$2\sqrt{14}$

$14\sqrt2$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{2})^2+(\sqrt{14})^2$

Simplify.

c^2=2+14

Solve.

c^2=16

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{16}$

Simplify.

c=4

Report an Error

Example Question #64 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{39}$

$3\sqrt{13}$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{3})^2+(\sqrt{13})^2$

Simplify.

c^2=3+13

Solve.

c^2=16

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{16}$

Simplify.

c=4

Report an Error

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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 #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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

Example Question #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #61 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #65 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #66 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #62 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #63 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #69 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #64 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

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