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Question
Is it possible to design a rectangular park of perimeter 320 m and area 4800 m2? If so find its length and breadth.
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Solution
Let the length of the rectangular park be “l”
and the breadth of the rectangular park be “b”
Perimeter of the park = 320 m
2 (l + b) = 320
l + b = 160
l = 160 – b ...(1)
Area of the park = 4800 m2
l × b = 4800 ...(2)
substitute the value of l = 160 – b in (2)
(160 – b)b = 4800
160b – b2 = 4800
b2 – 160b + 4800 = 0
(b – 120) (b – 40) = 0
b = – 120 = 0 or b – 40 = 0
b = 120 or b = 40
If breadth is 120 length is 40
If breadth is 40 length is 120
Length of the park = 120 m
Breadth of the park = 40 m
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