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 18  and the triangle has an area of 90 . What are the lengths of sides A and B?

May 7, 2016

A=B= ${\left(181\right)}^{\frac{1}{2}}$

Explanation:

Area of triangle is given by:

$\left(\frac{1}{2}\right)$ x (base) x (height) = 90

given that A=B, C is the base of the triangle ABC hence,

height = $\frac{90 \cdot 2}{18}$ = 10

Given that the height bisects the base C,
the side A and B can be found using Pythagoras's theorem,

A=B= ((18/2)^2 + (10)^2))^(1/2) = ${\left(181\right)}^{\frac{1}{2}}$