# How do you find the remaining sides of a 45^circ-45^circ-90^circ triangle if the longest side is 12?

Apr 9, 2018

The other two sides (they are equivalent in length) are $6 \sqrt{2}$ units

#### Explanation:

The longest side in a right triangle (a triangle with a 90 degree angle) is the hypotenuse.

45-45-90 triangle ratio of sides:

$1 : 1 : \sqrt{2}$

In other words, the hypotenuse can be found by multiplying the one of the side lengths by $\sqrt{2}$. The sides are the same length because the triangle is isosceles and right (has two angles of the same measure), and the smallest sides are the same.

That means that each of the smaller sides can be found by dividing the hypotenuse by the square root of 2.

$\frac{12}{\sqrt{2}} \rightarrow$ Rationalize the denominator (no radicals in the denominator)

$\frac{12 \cdot \sqrt{2}}{2}$

$6 \sqrt{2}$