Question

Rick's lumberyard has 360 yd of fencing with which to enclose a rectangular area. If the enclosed area is x yards​ long, express its area as a function of its length.

Answer 1

Answer:

180x - x²

Step-by-step explanation:

Since the yard has 360 yd. of fencing, hence the perimeter of Rick's lumberyard has 360 yd.

Given that the yard is x yards long. Let y represent the width of the yard. Hence:

Perimeter of the yard = 2(length + width) = 2(x + y)

Substituting:

360 = 2(x + y)

180 = x + y

y = 180 - x

Therefore the width of the yard is (180 - x) yard.

The area of the yard is the product of the length and the width, hence:

Area (A) = length * width

A = x * (180 - x)

A = 180x - x²