# In a 45°- 45°- 90° right triangle, the length of the hypotenuse is 15. How long are the legs?

Nov 13, 2015

$\frac{15 \sqrt{2}}{2}$

#### Explanation:

The legs and hypotenuse are in a $1 : \sqrt{2}$ ratio in this special triangle
so if the hypotenuse is 15 the legs are $\frac{15}{\sqrt{2}}$

you can think of it like this:

$\frac{x}{15} = \frac{1}{\sqrt{2}}$
$x = \frac{15}{\sqrt{2}}$

now to rationalize...
$\frac{15}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{15 \sqrt{2}}{2}$