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

Jan 28, 2017

$5.66$

#### Explanation:

First of all, we all know that if we cut the isosceles triangle into half we can have 2 right triangles.

The Given are:
$A = 16$ and
$b = 8$

The Area of the Triangle is
$A = \frac{b h}{2}$

Let's substitute the given to the formula:

$16 = \frac{8 h}{2}$

$16 = \frac{\cancel{8} h}{2}$

$16 = 4 h$

$\frac{16}{4} = \frac{4 h}{4}$

$\frac{16}{4} = \frac{\cancel{4} h}{\cancel{4}}$

$h = 4$

NOw, we have the height of our right triangle. We will get its hypotenuse and the hypotenuse is one of the leg of our isosceles triangle.

The formula in getting the hypotenuse is the Pythagorean Theorem:

$c = \sqrt{{a}^{2} + {b}^{2}}$

When we cut our isosceles triangle into half, definitely the base would be in half too, so our base is $4$. and our height is also $4$.
Let's substitute:

c=sqrt(4^2+4^2

$c = \sqrt{16 + 16}$

c=sqrt(32

$c = 5.66$

The hypotenuse is $5.66$ which is also the side of our isosceles triangle.