# How do you find the remaining sides of a 45^circ-45^circ-90^circ triangle if the longest sides are each 5sqrt2?

Mar 21, 2018

In a 45-45-90 triangle, the longest side has to be the hypotenuse. The other two sides would be the same (in this case, 5).

#### Explanation:

The ratio of the sides of an isosceles right triangle (45-45-90) is $1 : 1 : \sqrt{2}$ (leg:leg:hypotenuse). The hypotenuse is found by multiplying the length of the leg by $\sqrt{2}$.

To find the length of a leg from the hypotenuse, divide by $\sqrt{2}$

$\frac{5 \sqrt{2}}{\sqrt{2}} = 5$

Each of the legs are 5 units long