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Question
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Solution
Let the breadth of the rectangle be x meters. Then
Perimeter = 82 meters
2(length + breadth) = 82
(length + x) = 41
length = 41 - x
And area of the rectangle
length x bradth = 400
(41 - x)x = 400
41x - x2 = 400
x2 - 41x + 400 = 0
x2 - 25x - 16x + 400 = 0
x(x - 25) -16(x - 25) = 0
(x - 25)(x - 16) = 0
or
x - 16 = 0
x = 16
Since perimeter is 82 meter. So breadth can’t be 25 meter.
Hence, breadth 16 meters.
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