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CAT 2017 [slot 2] Question with solution 19

Question 53:
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
Answer: 200
Explanation:

Let the length and breadth of the park be l,b, l > b
Case 1: 2l + b = 400
Area = lb. Area is maximum when 2l × b is maximum, which is maximum when 2l = b (using AM $ \geq $ GM inequality) => l = 100, b = 200. Which can't happen since l > b

Case 2: l + 2b = 400
Area = lb. Area is maximum when l ×2 b is
maximum, which is maximum when l = 2b (using AM $ \geq $ GM
inequality) => l = 200, b = 100.

Hence length of the longer side is 200 ft


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