### Video Transcript

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. We can use 𝑥 to represent the
length of the barn, which will be more than 88 meters, and the width of the
rectangular barn will be represented by the variable 𝑦. However, we haven’t been told
anything specifically about 𝑦, but we know that the perimeter will be less than 253
meters. Thinking a bit more about the
perimeter of a rectangular sheep barn, if the length is 𝑥 and the width is 𝑦, we
know that the perimeter of a rectangle is equal to two times the length plus the
width.

The perimeter of the sheep barn must
be less than 253 meters. We know that two times the length
plus the width is equal to the perimeter. Therefore, we can say two times 𝑥
plus 𝑦 must be less than 253. Additionally, we know that the
length 𝑥 must be greater than 88 meters, which means we can write an inequality 𝑥
is greater than 88. You might think we’re finished as
we’ve described this system with two inequalities. However, we will also have to
define our width with one more inequality. We want to make sure that if we
were to solve this equation, we would only be dealing with positive values. And that means we have to define 𝑦
as greater than zero.

Therefore, the system of
inequalities that describes this situation is 𝑥 greater than 88, 𝑦 greater than
zero, and two times 𝑥 plus 𝑦 is less than 253.