A rectangle has an area of 96cm2. The width is four less than the length. What is the perimeter?
A: 100 cm
B: 75 cm
C: 60 cm
D: 40 cm
For a rectangle, area is A=lw and perimeter is P=2l+2w, where l is the length and w is the width.
Let x = length and x−4 = width.
The area equation to solve becomes x(x−4)=96, or x2−4x−96=0.
To factor, find two numbers the sum to -4 and multiply to -96. -12 and 8 will work:
x2 + 8x - 12x - 96 = 0
x(x + 8) - 12(x + 8) = 0
(x - 12)(x + 8) = 0
Set each factor equal to zero and solve:
x=12 or x=−8.
Therefore the length is 12cm and the width is 8cm, giving a perimeter of 40cm.
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