# 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 16  and the triangle has an area of 112 . What are the lengths of sides A and B?

Jun 20, 2016

Sides $A$ and $B$ have length of $\sqrt{260} = 2 \sqrt{65}$

#### Explanation:

From the given area $A = 112$ we can calculate the heigth:

$A = \frac{1}{2} \cdot a \cdot h$

$\frac{1}{2} \cdot 16 \cdot h = 112$

$8 h = 112$

$h = 14$

Now we can use the Pythagorean theorem to calculate the length of the equal sides:

${8}^{2} + {14}^{2} = {b}^{2}$

${b}^{2} = 64 + 196$

${b}^{2} = 260$

$b = 2 \sqrt{65}$