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

Mar 24, 2016

I found $14.77$

#### Explanation:

Consider the diagram:

The Area is given as:

"Area"=("Base"xx"Height")/2(CxxH)/2=81

So:

$\frac{12 \cdot H}{2} = 81$
$H = \frac{81}{6} = 13.5$

We use half triangle and Pythagoras:

${A}^{2} = {H}^{2} + {\left(\frac{C}{2}\right)}^{2} = {H}^{2} + {C}^{2} / 4 = {13.5}^{2} + {12}^{2} / 4 = 182.25 + 36 = 218.25$

and:

$A = \sqrt{218.25} = 14.77 = B$