Question

A rectangle has a perimeter of 44 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle?

Answer 1

• A rectangle has a perimeter of 44 inches and an area of 72 square inches.
• Perimeter = 44 inches, area = 72 square inches.
• Let the length and breadth be l and b respectively.
• We know, perimeter of a rectangle = 2(l + b)
• Therefore,
• 2(l + b) = 44

or, l + b = 22

or, b = 22 - l ...(i)

• We know, area of a rectangle = lb
• Therefore,
• lb = 72
• Putting (i) in b, we get
• l(22 - l) = 72

or, 22l - l^2 -72 = 0

or, l^2 - 22l + 72 = 0

or, l^2 - 4l - 18l + 72 = 0

or, l(l - 4) - 18(l - 4) = 0

or, (l - 4)(l - 18) = 0

or, l = 4 or l = 18

• Therefore, if the length is 4 inches, then the breadth is (22-4) inches, i.e., 18 inches.
• And if the length is 18 inches, then the breadth is (22-18) inches, i.e., 4 inches.

Answer:

B) 4 inches and 18 inches.

Hope you could get an idea from here.

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