# In a 45-45-90 triangle, one of the legs is 2sqrt2. What is the length of the hypotenuse?

Dec 4, 2015

4

#### Explanation:

The triangles with two equal sides are isosceles triangles.
Let the length of hypotenuse be $a$?
${\left(2 \sqrt{2}\right)}^{2} + {\left(2 \sqrt{2}\right)}^{2} = {a}^{2}$
$\implies {a}^{2} = 8 + 8$
$\implies {a}^{2} = 16$
$\implies {\sqrt{a}}^{2} = \sqrt{16}$
$\implies a = 4$