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

Oct 8, 2016

The length of sides $A \mathmr{and} B$ are $8.49 \left(2 \mathrm{dp}\right) u n i t$ each .

#### Explanation:

Side $C$ is the base of the isoceles triangle, $A \mathmr{and} B$ are legs, and $x$ be the altitude.
The area of triangle is ${A}_{t} = \frac{1}{2} \cdot C \cdot x \mathmr{and} 36 = \frac{1}{2} \cdot 12 \cdot x \mathmr{and} x = 6$
$= \left({A}^{2} - {\left(\frac{C}{2}\right)}^{2}\right) = {x}^{2} \mathmr{and} \left({A}^{2} - {\left(\frac{12}{2}\right)}^{2}\right) = 36 \mathmr{and} {A}^{2} - 36 = 36 \mathmr{and} {A}^{2} = 72 \mathmr{and} A = \sqrt{72} = \pm 8.485$.
Side can not be negative.

So the length of sides $A \mathmr{and} B$ are $8.49 \left(2 \mathrm{dp}\right) u n i t$ each.[Ans]