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
[tex]l = 2w[/tex]
Perimeter = 30 feet
[tex]\text{Perimeter of rectangle} = 30\\2\times (l\times w) = 30[/tex]
Putting values,
[tex]2(2w + w) = 30\\6w = 30\\w = 5\\l = 2w = 10[/tex]
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 =
[tex]=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[/tex]
Thus, $57.5 is the total cost to build the pen.
