An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse?

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An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse?

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Answer 1 · 2015-11-14T03:28:12

$c = \sqrt{32}$ $c = sqrt(32)$

Explanation:

We will use the Pythagorean Theorem for this problem.

We know that each leg is $4 c m$ $4cm$ . We can plug those in for $a$ $a$ and $b$ $b$ , to find our hypotenuse, $c$ $c$ .

$4^{2} + 4^{2} = c^{2}$ $4^2 + 4^2 = c^2$
$16 + 16 = c^{2}$ $16 + 16 = c^2$
$32 = c^{2}$ $32 = c^2$
$c = \sqrt{32}$ $c = sqrt(32)$

Answer 2 · 2015-11-14T03:31:26

$4 \sqrt{2} cm$ $4sqrt(2)"cm"$

Explanation:

By the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's legs. That is, for a right triangle with legs $a$ $a$ and $b$ $b$ and hypotenuse $c$ $c$
$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

In this case, we have $a = b = 4 cm$ $a = b = 4"cm"$ , thus

$c^{2} = {(4 cm)}^{2} + {(4 cm)}^{2} = 32 {cm}^{2}$ $c^2 = (4"cm")^2 + (4"cm")^2 = 32"cm"^2$

$\Rightarrow c = \sqrt{32 {cm}^{2}} = \sqrt{16 \cdot 2} cm = 4 \sqrt{2} cm$ $=> c = sqrt(32"cm"^2) = sqrt(16*2)"cm" = 4sqrt(2)"cm"$

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An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse?

2 Answers

Explanation:

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