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 `8` and the triangle has an area of `32`. What are the lengths of sides A and B?

Answer 1

`sqrt80`

Explanation:

Area of a triangle `A=1/2*b*h`, where `b` is the base and `h` is the height.

Given that `A=B`, base `C=8`, and area of the triangle `=32`,
`=> 32=1/2*8*h`
`=> h=8`

`A^2=h^2+(C/2)^2`

`=> A=sqrt(8^2+(8/4)^2)=sqrt80`

Hence, `A=B=sqrt80`