mathschallenge.net

Problem

An equilateral triangle is circumscribed.

Find the area of the triangle.

Solution

Consider the following diagram.

Using the Pythagorean Theorem, 4$x$² = $x$² + 9
3$x$² = 9 $x$ = 3.

Area of triangle is 33.

It can be seen that the perimeter of the triangle is 63, i.e. double the area. What radius circle would have a circumscribed equilateral triangle with an area the same size as the perimeter?