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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 #114 : Geometry

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

Possible Answers:

$\displaystyle 6$

$\sqrt{33}$ $\displaystyle \sqrt{33}$

$\sqrt{35}$ $\displaystyle \sqrt{35}$

$\sqrt{34}$ $\displaystyle \sqrt{34}$

Correct answer:

$\sqrt{34}$ $\displaystyle \sqrt{34}$

Explanation:

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

For any triangle with leg lengths of $\displaystyle a$ and $\displaystyle b$,

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

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

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

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

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

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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:

$\displaystyle 8$

$\sqrt{65}$ $\displaystyle \sqrt{65}$

$\sqrt{66}$ $\displaystyle \sqrt{66}$

$\sqrt{69}$ $\displaystyle \sqrt{69}$

Correct answer:

$\sqrt{65}$ $\displaystyle \sqrt{65}$

Explanation:

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

For any triangle with leg lengths of $\displaystyle a$ and $\displaystyle b$,

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

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

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

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

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

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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:

$\sqrt{15}$ $\displaystyle \sqrt{15}$

$4\sqrt2$ $\displaystyle 4\sqrt2$

$3\sqrt3$ $\displaystyle 3\sqrt3$

$\sqrt{14}$ $\displaystyle \sqrt{14}$

Correct answer:

$\sqrt{14}$ $\displaystyle \sqrt{14}$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

c^2=6+8 $\displaystyle c^2=6+8$

Solve.

c^2=14 $\displaystyle c^2=14$

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

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

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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:

$\displaystyle 5$

$6\sqrt2$ $\displaystyle 6\sqrt2$

$4\sqrt5$ $\displaystyle 4\sqrt5$

$\sqrt{26}$ $\displaystyle \sqrt{26}$

Correct answer:

$\displaystyle 5$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=6+19$

Solve.

c^2=25 $\displaystyle c^2=25$

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

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

Simplify.

c=5 $\displaystyle c=5$

Report an Error

Example Question #293 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$\displaystyle 5$

$2\sqrt3$ $\displaystyle 2\sqrt3$

$2\sqrt6$ $\displaystyle 2\sqrt6$

$5\sqrt2$ $\displaystyle 5\sqrt2$

Correct answer:

$\displaystyle 5$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=11+14$

Solve.

c^2=25 $\displaystyle c^2=25$

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

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

Simplify.

c=5 $\displaystyle c=5$

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:

$\displaystyle 5$

$3\sqrt3$ $\displaystyle 3\sqrt3$

$4\sqrt2$ $\displaystyle 4\sqrt2$

$\sqrt{26}$ $\displaystyle \sqrt{26}$

Correct answer:

$\sqrt{26}$ $\displaystyle \sqrt{26}$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=10+16$

Solve.

c^2=26 $\displaystyle c^2=26$

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

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

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:

$\displaystyle 8$

$8\sqrt3$ $\displaystyle 8\sqrt3$

$\displaystyle 7$

$6\sqrt5$ $\displaystyle 6\sqrt5$

Correct answer:

$\displaystyle 7$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=10+39$

Solve.

c^2=49 $\displaystyle c^2=49$

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

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

Simplify.

c=7 $\displaystyle c=7$

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:

$\displaystyle 7$

$16\sqrt2$ $\displaystyle 16\sqrt2$

The length of the hypotenuse cannot be determined.

$4\sqrt6$ $\displaystyle 4\sqrt6$

Correct answer:

$\displaystyle 7$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=20+29$

Solve.

c^2=49 $\displaystyle c^2=49$

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

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

Simplify.

c=7 $\displaystyle c=7$

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:

$2\sqrt{14}$ $\displaystyle 2\sqrt{14}$

$\displaystyle 4$

$14\sqrt2$ $\displaystyle 14\sqrt2$

$4\sqrt{14}$ $\displaystyle 4\sqrt{14}$

Correct answer:

$\displaystyle 4$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=2+14$

Solve.

c^2=16 $\displaystyle c^2=16$

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

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

Simplify.

c=4 $\displaystyle c=4$

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:

$3\sqrt{13}$ $\displaystyle 3\sqrt{13}$

$\sqrt{39}$ $\displaystyle \sqrt{39}$

$\displaystyle 4$

$\displaystyle 3$

Correct answer:

$\displaystyle 4$

Explanation:

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

$\displaystyle a^2+b^2=c^2$

Substitute in the given values.

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

Simplify.

$\displaystyle c^2=3+13$

Solve.

c^2=16 $\displaystyle c^2=16$

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

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

Simplify.

c=4 $\displaystyle c=4$

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 #114 : Geometry

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

Example Question #293 : Triangles

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 #63 : 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

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

All Basic Geometry Resources

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