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

Answer 1

`sqrt257~~16.03`

Explanation:

First things first - we start off with a diagram!

Not the most elegant diagram in the world, but it does the job. By convention, the side opposite angle `A` is `a`, opposite angle `B` is `b` and `C` is `c`. `h` is the perpendicular bisector of AB at M - it cuts AB in half at a right angle.

Let `a=b=x`. Our job is to find `x`.

`Area_triangle=1/2bh`
`16=1/2xx32h`
`16=16h`
`h=1`

Now, we can apply Pythagoras' Theorem in one of the right-angled triangles. We have the height `h=1` and the base`=16`, so we can work out x.

`1^2+16^2=x^2`
`1+256=x^2`
`x^2=257`
`x=sqrt257~~16.03`