# An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 12  and the triangle has an area of 64 . What are the lengths of sides A and B?

Apr 11, 2016

$\left\mid A \right\mid = \left\mid B \right\mid \approx 12.24$

#### Explanation:

$\frac{1}{2} \times 6 \times h = \frac{1}{2} \times \text{Area}$

$\Rightarrow h = \frac{64}{6}$

and, by Pythagorean Theorem
$\textcolor{w h i t e}{\text{XXX}} \left\mid A \right\mid = \left\mid B \right\mid = \sqrt{{\left(\frac{64}{6}\right)}^{2} + {6}^{2}}$
$\textcolor{w h i t e}{\text{XXXXXXXXX}} \approx 12.24$