# In a right- angled triangle, the two sides that form the right angle are both 5 inches. How do you find the length of the other side (the hypotenuse)?

Jun 14, 2018

$5 \sqrt{2}$ inches

#### Explanation:

Given: A right triangle with two sides $5$ inches.

To find the hypotenuse you can use the Pythagorean Theorem:

${5}^{2} + {5}^{2} = {h}^{2}$, where $h$ is the hypotenuse

$h = \sqrt{25 + 25} = \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \sqrt{2} = 5 \sqrt{2}$

The other way to solve is to realize that a ${45}^{\circ} - {45}^{\circ} - {90}^{\circ}$ triangle has the side proportions: $1 : 1 : \sqrt{2}$

This means if the sides are $5$ inches, the sides would be: $5 : 5 : 5 \sqrt{2}$