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
Explanation:
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.
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