Question:
If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
Updated On: Dec 31, 2025
- 150
- 100
- 200
- 350
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The Correct Option is C
Solution and Explanation
Let one side be l and the other be b. (l is not necessarily greater than b)
Given, 2l + b = 400
For area to be maximum, lb should be maximum.
∴ l (400 – 2l) should be maximum
l (400 – 2l) = l (2) (200–l) = 2 (l) (200 – l)
l (200 – l) will be maximum when l = 200 – l or 2l = 200
⇒ l = 100
If l = 100, b = 200.
∴ The longer side must be 200 feet long.
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