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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.
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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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