What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 2 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 2 and 16?

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Answer 1 · 2015-12-28T01:45:04

$c = 2 \sqrt{65}$ $c=2sqrt65$

Explanation:

Use the Pythagorean theorem, $c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$ , where $c$ $c$ is the hypotenuse, and $a$ $a$ and $b$ $b$ are the other two sides.

Let side $a = 2$ $a=2$ and side $b = 16$ $b=16$ .

Substitute the given values into the equation.

$c^{2} = 2^{2} + 16^{2}$ $c^2=2^2+16^2$

Simplify.

$c^{2} = 4 + 256$ $c^2=4+256$

Simplify.

$c^{2} = 260$ $c^2=260$

Take the square root of both sides.

$c = \sqrt{260}$ $c=sqrt260$

Determine the prime factors of $260$ $260$ .

$c = \sqrt{2 \times 2 \times 5 \times 13}$ $c=sqrt(2xx2xx5xx13)$

Group identical factors.

$c = \sqrt{(2 \times 2) \times 5 \times 13}$ $c=sqrt((2xx2)xx5xx13)$

Rewrite $(2 \times 2)$ $(2xx2)$ as $2^{2}$ $2^2$ .

$c = \sqrt{2^{2} \times 5 \times 13}$ $c=sqrt(2^2xx5xx13)$

Apply the square root rule $\sqrt{a^{2}} = a$ $sqrt(a^2)=a$ .

$c = 2 \sqrt{5 \times 13}$ $c=2sqrt(5xx13)$

Simplify.

$c = 2 \sqrt{65}$ $c=2sqrt65$

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What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 2 and 16?

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