Answer:
Length = 32 feet
Width = 10 feet
Step-by-step explanation:
The area of a rectangle = length (L) x width (W)
The relationship between the length and width is that
L = 12 + 2W -------------- (i)
therefore
Area = L x W can be rewritten as (12 + 2W) x W
320 = (12 + 2W) x W
320 = 12W + 2W^2
this can then be turned into a quadratic equation:
2W^2 + 12W - 320 = 0
Divide through by 2
W^2 + 6W - 160 = 0
W^2 - 10W + 16W - 160 = 0
W(W- 10) + 16(W- 10) = 0
(W- 10)(W + 16) = 0
hence W = -16 and 10
since width cannot be a negative value,
Width = 10
hence substituting for width = 10 into equation (i)
L = 12 + 2(10)
L = 12 +20 = 32
