A shepherd wants to build a rectangular sheep barn. The length of the barn must be more than 88 meters, and its perimeter must be less than 253 meters. Derive the system of inequalities that describes the situation, denoting the length of the barn by 𝑥 and its width by 𝑦.
Let’s start by highlighting what we know. The length of the barn is represented by 𝑥. The width of the barn is represented by 𝑦. We know that the length of the barn must be more than 88 meters. We can translate that into an inequality that says 𝑥 must be greater than 88 meters. The barn’s perimeter must be less than 253 meters. Perimeter must be less than 253 meters.
What is the formula for finding the perimeter of a rectangle? Usually, we write the formula like this: two times the length plus the width. But our instructions gave us variables that we should use for the length and the width. Instead of 𝑙 for the length, we should put in 𝑥. Instead of 𝑤 for the width, we’ll include 𝑦.
This inequality would then read: two times 𝑥 plus 𝑦 must be less than 253 meters. Here are two inequalities that describe the situation of the shepherd and his sheep barn.