# What is the height of an isosceles triangle whose base is 10 and whose equal sides are 20?

Feb 19, 2017

Height: $5 \sqrt{15}$

#### Explanation:

The perpendicular bisector divides the base into segments of length $5$ each.

Using the Pythagorean Theorem:
$\textcolor{w h i t e}{\text{XXX}} {\textcolor{b l u e}{5}}^{2} + {\textcolor{g r e e n}{h}}^{2} = {\textcolor{red}{20}}^{2}$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{h} = \sqrt{\textcolor{red}{400} - \textcolor{b l u e}{25}} = 5 \sqrt{15}$