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I assume the carpet has the shape of a rectangle. Let L = length Let W = width The area is 192 ft^2. LW = 192 The perimeter is 56 ft. 2L + 2W = 56 We have a system of 2 equation in 2 unknowns. LW = 1922L + 2W = 56 Divide the second equation by 2: L + W = 28 Subtract W from both sides. L = 28 - W Substitute 28 - W for L in the first equation. LW = 192 (28 - W)W = 192 28W - W^2 = 192 W^2 - 28W + 192 = 0 (W - 12)(W - 16) = 0 W - 12 = 0  or  W - 16 = 0 W = 12 or W = 16 L = 28 - W For W = 12: L = 28 - 12 = 16 For W = 16" L = 28 - 16 = 12 We get: length = 16 and width = 12 or: length = 12 and width = 16 Either answer is correct, but since people think the length is longer than the width, answer with a longer length than the width. Answer: Length = 16 ft   Width = 12 ft


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