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

Nov 14, 2015

$c = \sqrt{32}$

#### Explanation:

We will use the Pythagorean Theorem for this problem.

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

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

Nov 14, 2015

$4 \sqrt{2} \text{cm}$

#### 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 $a$ and $b$ and hypotenuse $c$
${a}^{2} + {b}^{2} = {c}^{2}$

In this case, we have $a = b = 4 \text{cm}$, thus

c^2 = (4"cm")^2 + (4"cm")^2 = 32"cm"^2

=> c = sqrt(32"cm"^2) = sqrt(16*2)"cm" = 4sqrt(2)"cm"