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 `88`. What are the lengths of sides A and B?

Answer 1

`abs(A)=abs(B)=10sqrt(5)`

Explanation:

Viewing C as the base and denoting the height as `h`
the formula for the area of a triangle tell us that:
`color(white)("XXX")1/2*8*h=88` (using the given values)

This implies that `h=22`

Side A (or B) together with half the length of C and the height form a right-angled triangle (with A the hypotenuse).

Therefore
`color(white)("XXX")abs(A)=sqrt(4^2+22^2)=sqrt(500)=10sqrt(5)`