Question

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?

Answer 1

A=B= `(181)^(1/2)`

Explanation:

Area of triangle is given by:

`(1/2)` x (base) x (height) = 90

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

height = `(90*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)` = `(181)^(1/2)`