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 `32` and the triangle has an area of `108`. What are the lengths of sides A and B?

Answer 1

`=17.37`

Explanation:

This is an isosceles triangle with `base=32` and `height=h`
Area of a triangle`=1/2times32timesh=108`
or
`=h=108times2/32=6.75`
In isosceles triangle `h` divides `base` equally
In other words isosceles triangle is 2 equal right-angled triangle combined with each right-angled triangle having `b=32/2=16 and p =6.75`
So side`A`=side `B=sqrt(16^2+6.75^2)=17.37`