The dimensions of the coop are length = 12 ft and width = 9 ft
<h3>Area of the coop</h3>
Since the coop is a rectangle, the area of the coop is A = LW where
- L = length of coop and
- W = width of coop.
Now, the length of the coop 3 feet longer than the width, so, L = W + 3
Now, the area of the coop A = 108 ft²
So, A = LW
A = (W + 3)W
108 = W² + 3W
Re-arranging,
W² + 3W - 108 = 0
So, we solve the equation to find the width of the coop
<h3>
Width of coop</h3>
W² + 3W - 108 = 0
Factorizing, we have
W² + 12W - 9W - 108 = 0
W(W + 12) - 9(W + 12) = 0
(W + 12)(W - 9) = 0
W + 12 = 0 or W - 9 = 0
W = -12 or W = 9
Since W cannot be negative, W = 9
<h3>
Length of coop</h3>
Since L = W + 3
Substituting the value of W into L, we have
L = W + 3
L = 9 + 3
L = 12 ft
So, dimensions of the coop are length = 12 ft and width = 9 ft
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