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 60 feet. Ifthe material used to build the pen is $1.75 per foot for the longer sides and $2.50 per foot for the shorter sides(the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.It costs $to build the fence.

Answer 1

It costs $120 to build a fence.

Step-by-step explanation:

We first need to find the length of the longer side and the shorter side of the rectangle. So, let's call x the length of the rectangle and y the width of the rectangle.

If the rectangle is 2 times as long as it is wide, we can write the following equation:

x = 2y

If the perimeter is 60 feet, we can write the equation

2x + 2y = 60

Then, replacing the first equation on the second and solving for x, we get:

2x + x = 60

3x = 60

3x/3 = 60/3

x = 20 feet

Now, we can find the value of y

x = 2y

20 = 2y

20/2 = 2y/2

10 = y

Therefore, the length of the rectangle is 20 feet and the width is 10 feet.

Now, we can calculate the cost, multiplying the longer sides by $1.75 and the shorter sides by $2.5, so

C = 20(1.75) + 20(1.75) + 10(2.5) + 10(2.5)

C = 120

So, it costs $120 to build a fence.