Question

Cisco and Misty need to construct a chicken coop for their famous egg-laying hens. The hens need at least 108 square feet of living space. The space available allows Cisco and Misty to make the length of the coop 3 feet longer than the width and to create exactly 108 square feet of area. What are the dimensions of the coop?

Answer 1

The dimensions of the coop are length = 12 ft and width = 9 ft

Area of the coop

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

Width of coop

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

Length of coop

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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