Question
Quantitative Aptitude Question on Mensuration
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
A
150
B
100
C
200
D
350
Answer
200
Explanation
Solution
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.