# 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 #40 #. What are the lengths of sides A and B?

##### 2 Answers

Side A = Side B = 10.77 units

#### Explanation:

Let side A=side B=

Then drawing a right-angled triangle, with

Using pythagoras theorem,

But since h is a length, it can only be positive

Area of triangle =

But since x is a side, then it can only be positive

#### Explanation:

Hey, small letters for triangle sides.

Isosceles triangle

Let's see if we can do this different ways. First, the way the teacher probably expects:

The foot

Let's just do it directly from Archimedes' Theorem:

The sides can be arbitrarily interchanged; I picked the form that gets some cancelling when

That was easier.