# In an isosceles triangle, the perpendicular bisected of one leg passes thru the midpoint of the base. If the leg is 10, how long is the base?

Mar 27, 2018

20

#### Explanation:

if the diagram i have is correct then the answer is 20.

because
in $\triangle A D C$ $\angle C$ is ${90}^{\circ}$ and $\angle D$ is ${90}^{\circ}$ so the $\angle D A C = 180 - 45 - 90 = {45}^{\circ}$
in an isosceles triangle the perpendicular from the top to the bottom will bisect the bottom line.
as $\triangle A D C$ is a isosceles triangle $A D = D C$
so, $D C = 10$
therefore, the length of the total base is $10 + 10 = 20$