# In a 45°- 45°- 90° right triangle, the length of the hypotenuse is 12. How long are the legs?

Jul 1, 2015

I found $8.5$

#### Explanation:

You can use Pythagoras Theorem where $c = 12$ is the hypotenuse and the other two legs have the same length $a$ (it is an isosceles triangle=two equal sides); so:
${c}^{2} = {a}^{2} + {a}^{2}$
${12}^{2} = 2 {a}^{2}$
$144 = 2 {a}^{2}$
${a}^{2} = 72$
$a = \pm \sqrt{72} = \pm 8.5$
You choose the positive one.