If the side length of a square is
equal to the side length of an equilateral triangle, what is the ratio of the
perimeter of the square to the perimeter of the equilateral triangle?
Let’s begin by drawing our two
shapes. If we let the side length of the
square be equal to 𝐿, then its perimeter will be equal to four 𝐿. We are told that the side length of
an equilateral triangle is the same. This means it will have a perimeter
of three 𝐿. The ratio of the perimeter of the
square to the triangle is therefore four 𝐿 to three 𝐿. Dividing both of these by 𝐿 gives
a ratio in its simplest form of four to three.