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Question
The perimeter of a rectangle is 104 m and its area is 640 m2. Find its length and breadth.
Solution
Let the length and the breadth of the rectangle be x m and y m.
Perimeter = 2(x + y) m
∴ 104 = 2(x + y)
x + y = 52
y = 52 – x
Area = 640 m2
∴ xy = 640
x(52 – x) = 640
x2 – 52x + 640 = 0
x2 – 32x – 20x + 640 = 0
x(x – 32) – 20(x – 32) = 0
(x – 32)(x – 20) = 0
x = 32, 20
When x = 32, y = 52 – 32 = 20
When x = 20, y = 52 – 20 = 32
Thus, the length and breadth of the rectangle are 32 m and 20 m.
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