Write this ratio in its simplest form: The ratio of the perimeter of a rhombus to its side length.
In order to write a ratio, we write numerical values separated by a colon. The order of the numbers is particularly important. In this case, because we’re asked for the perimeter of a rhombus to its side length, the first number will refer to the perimeter and the second number will refer to side length. So let’s begin by drawing a rhombus of side length 𝑥.
Since a rhombus is a quadrilateral with all four sides equal, then we know that the other three lengths on our rhombus will also be of length 𝑥. Since the perimeter of a shape is the distance from the outside, we can calculate the perimeter of the rhombus by adding 𝑥 plus 𝑥 plus 𝑥 plus 𝑥, which will give us four 𝑥.
In order to write the ratio of perimeter to side length, we can begin by writing four 𝑥 to 𝑥. But since we only want numerical values in our ratio, we’re going to divide both sides of our ratio by 𝑥. And this will give us our final answer for our ratio of the perimeter of a rhombus to the side length as four to one.