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
