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

• A. 150
• B. 100
• C. 200
• D. 350

Answer 1

The Correct Option is C

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.