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Question 19 : 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 [TITA]


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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 2 Geometry

Given that the three sides of a rectangular park have a total length 400ft
i.e. 2x + y = 400 ft
xy should be maximum
y = 400 – 2x
x × (400 – 2x) = max
x × (200 – x) = max
Let us check for different values
CAT 2017 Question Paper Quants Slot 2 Geometry
The area of the park is maximum when x = 100 and y = 200.
The length of the longer side y is equal to 200 ft.

The question 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 [TITA]"

Hence, the answer is 200

 

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