Answer:
Length = 45 ft and Width = 15 ft
Step-by-step explanation:
We have three pens, and they share a common side, which will be the bigger side, so we have the maximum benefit from the fencing.
If we call L the length and W the width of the pens, we have:
(See the figure attached for better understanding)
6W + 4L = 360
Total area = L * 3W
From the first equation:
3W + 2L = 180
W = (180 - 2L)/3
Using this value of W in the area equation:
Area = L * (180 - 2L) = 180L - 2L2
to find the maximum area, we need to find the vertix of the quadratic equation:
L = -b/2a (a and b are coefficients of the quadratic equation: a = -2 and b = 180)
L = -180/(-4) = 45 ft
Now we can find the width:
W = (180 - 3*45)/3 = 15 ft
So we have length = 45 ft and width = 15 ft
