Question

A livestock pen is built in the shape of a rectangle that is 2 times as long as it is wide. The perimeter is 30 feet. If the material used to build the pen is $ 1.75 per foot for the longer sides and $ 2.25 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.

Answer 1

Answer:

$57.5 is the total cost to build the pen.

Step-by-step explanation:

We are given the following in the question:

A livestock pen is built in the shape of a rectangle.

The length of rectangle is two times the width.

Let l be the length of rectangle and w be the width of rectangle. Thus, we can write

$l = 2w$

Perimeter = 30 feet

$\text{Perimeter of rectangle} = 30\\2\times (l\times w) = 30$

Putting values,

$2(2w + w) = 30\\6w = 30\\w = 5\\l = 2w = 10$

The length of rectangle is 10 feet and width of rectangle is 5 feet.

If the material used to build the pen is $ 1.75 per foot for the longer sides and $ 2.25 per foot for the shorter sides

Cost of building =

$=2\times(\text{Cost of length}\times \text{Length} + \text{Cost of width}\times \text{Width})\\=2\times(1.75\times 10 + 2.25\times 5)\\=57.5$

Thus, $57.5 is the total cost to build the pen.