Question

Giselle and Brian are building a rectangular fence at a dog park as a community service project. They have 145 yards of fencing material to use. The length of the fenced area is 2 more than three times the width. What is the length of the fenced area?​

Answer 1

The length of the fenced area that Giselle and Brian are building for a dog park is 54.875 yards. This length is calculated using the total amount of fencing and the given relationship between the length and width of the rectangle.

Step-by-step explanation:

Giselle and Brian have 145 yards of fencing to use for a rectangular fence. The perimeter of a rectangle is calculated by the formula 2(length + width). According to the problem, the length is 2 yards more than three times the width. Let's denote the width as w and the length as l. Then, l = 3w + 2.

Now we can set up the equation for the perimeter using the given total amount of fencing:
2(w + l) = 145 yards
2(w + 3w + 2) = 145
2(4w + 2) = 145
8w + 4 = 145.

To find the width (w), we solve:
8w = 145 - 4
8w = 141
w = 141 / 8
w = 17.625 yards.

Now we substitute the width back into the length formula to find the length (l):
l = 3(17.625) + 2
l = 52.875 + 2
l = 54.875 yards.

Therefore, the length of the fenced area is 54.875 yards.