# 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 64 . What are the lengths of sides A and B?

Oct 8, 2016

$8 \sqrt{2} = 11.3137$

#### Explanation:

Given $A = B , C = 16$, Area ${A}_{r} = 64$,

$\implies {A}_{r} = \frac{1}{2} \cdot C \cdot h$
$\implies 64 = \frac{1}{2} \cdot 16 \cdot h , \implies h = 8$

${A}^{2} = {h}^{2} + {\left(\frac{C}{2}\right)}^{2}$

$\implies {A}^{2} = {8}^{2} + {\left(\frac{16}{2}\right)}^{2} = {8}^{2} + {8}^{2} = 128$

$\implies A = \sqrt{128} = \sqrt{64 \cdot 2} = 8 \sqrt{2} = 11.3137$

Hence, $A = B = 11.3137$