CAT 2017 Slot 2 — QA Question 19
Basics of Mensuration/PrismEasy
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 & solution
Answer: 200
Solution
Let ‘x’ and ‘y’ be the dimensions of the rectangle
Let us suppose 2x + y = 400 … (1)
Area = xy.
For xy to be maximum, 2xy should also be maximum.
Now the product 2xy will be maximum when 2x = y. [AM ≥ GM]
So y + y = 400 [From (1)]
⇒ 2y = 400 or y = 200
Substituting value of y in (1) we get,
2x = 200 or x = 100
In a rectangle, length is greater than breadth, so we take y as the length.
Hence area of the park is maximum when length is 200 ft.
Hence, 200.