An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the area of the triangle to the area of the square? Express your answer as a common fraction.
The equilateral triangle will each have side lengths of 16 and the square will have all its side lengths of 12.
The area of the square is 12^2
We know that the altitude of the equilateral triangle is 8sqrt(3) by the 30-60-90 we form when dividing the triangle in half. Therefore, the area of the eqilateral triangle is 64sqrt(3)
Therefore, the ratio will be
64sqrt(3)/144, which simplifies to 4sqrt(3)/9