# 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 4  and the triangle has an area of 36 . What are the lengths of sides A and B?

May 30, 2016

The equal sides of the triangle are $\sqrt{328} = 2 \sqrt{82} \approx 18.1$ units long

#### Explanation:

Using the information about triangle's area we have:

$A = 36$

$\frac{1}{2} \cdot 4 \cdot h = 36$

$2 h = 36$

$h = 18$

Now we can calculate the remaining side using Pythagorean Theorem:

${2}^{2} + {18}^{2} = {b}^{2}$

$4 + 324 = {b}^{2}$

${b}^{2} = 328$

$b = \sqrt{328} = 2 \sqrt{82} \approx 18.1$