What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 8 and 16?

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What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 8 and 16?

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Answer 1 · 2018-05-02T02:46:28

$c = 8 \sqrt{5}$ $c = 8sqrt5$ or about $17.89$ $17.89$

Explanation:

The Pythagorean Theorem is:
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where $a$ $a$ and $b$ $b$ are the side lengths and $c$ $c$ is the hypotenuse.

In this question, we have the side lengths of $8$ $8$ and $16$ $16$ , we we can plug them into the Pythagorean Theorem and solve for the hypotenuse:
$c^{2} = 8^{2} + 16^{2}$ $c^2 = 8^2 + 16^2$

Simplify:
$c^{2} = 64 + 256$ $c^2 = 64 + 256$

$c^{2} = 320$ $c^2 = 320$

Take the square root of both sides:
$c = \sqrt{320}$ $c = sqrt320$

$c = \sqrt{64 \cdot 5}$ $c = sqrt(64 * 5)$

$c = 8 \sqrt{5}$ $c = 8sqrt5$ or about $17.89$ $17.89$ (rounded to nearest hundredth's place)

Hope this helps!

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What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 8 and 16?

1 Answer

Explanation:

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