2021 April MIMC 10 Problems/Problem 6
A worker cuts a piece of wire into two pieces. The two pieces, and , enclose an equilateral triangle and a square with equal area, respectively. The ratio of the length of to the length of can be expressed as in the simplest form. Find .
There are several different ways to solve this problems. For the sake of convenience, we can substitute a side length of the equilateral triangle. Let be the side length, then the area of the equilateral triangle is . The side length of the square can be solved by computing . However, the question is asking for the perimeter of triangle the perimeter of the square. Therefore, the ratio is . .