Answer:
20 ft long; 12 ft wide
Step-by-step explanation:
Let w = the width of the garden
Then l = w + 8
A = lw
A = (w + 8)w
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The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:
Width = w +8
Length = w + 16
Area = (w + 8)(w + 16)
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The difference between the two areas is the area of the sidewalk (320 ft²).
(w + 8)(w + 16) - (w + 8)w = 320 Factor out w + 8
(w+ 8)(w + 16 – w) = 320 Combine like terms
(w+ 8) × 16 = 320 Divide each side by 16
w + 8 = 20 Subtract 8 from each side
w = 12 ft
l = 12 + 8
l = 20 ft
The garden is 20 ft long by 12 ft wide.
