Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed
LW^2
The rectangle has an area of 96cm2. This means that
LW = 96 - - - - - - - - - - 1
The width is four less than the length. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W(W + 4)= 96
W^2 + 4W = 96
W^2 + 4W - 96 = 0
W^2 + 12W - 8W - 96 = 0
W(W + 12) - 8(W + 12) = 0
(W + 12)(W - 8) = 0
W = 8 or W = -12
Since the width cannot be negative, the W = 8cm
L = W + 4 = 8 + 4 = 12 cm
The formula for determining the perimeter of a rectangle is
Perimeter = 2(L + W)
Perimeter = 2(8 + 12) =2×20
Perimeter of rectangle = 40 cm
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