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

Answer 1

`abs(A)=abs(B)~~6.02` (units)

Explanation:

If `triangle_(ABC)` has a base of side `C` and `abs(A)=abs(B)`
then, given an area of `36` (square units),
the triangle must have a height (relative to the base `C`)
`color(white)("XXX")h=36/abs(C)=36/8=4.5`

Dividing the triangle into two right angled triangles as in the image below:

and using the Pythagorean Theorem:
`color(white)("XXX")abs(A)=abs(B)=sqrt(4^2+(4.5)^2)=sqrt(145)/2~~6.02`