Let the side of the triangle be , the side of the square be , and the radius of the circle be .Originally Posted by wardreese
Then the area of the equilateral triangle (by Herons formula - google for
it if you don't know it) is:
The area of the circle is:
and the area of the square is:
We are told that:
which allows us to write and in terms of .
We are also told that:
which when we replace and with what they are in terms of we are left with
a single linear equation for which is trivial to solve.