Question

If three sides of a rectangular park have a total length of 400ft, then the area of the park is maximum when the length (in ft) of its longer side is (in ft.)___

Answer 1

Let the sides of the rectangle be ‘a’ and ‘b’.
Now, we have to maximize area of the rectangle.
Area of the rectangle = ab, means we have to maximize ab.
Then according to question, 2a + b = 400.
ab is maximum when 2ab is maximum.
2ab is maximum when 2a = b, as 2a + b = 400 (Given)
So, 2a = b = 400/2 = 200
Hence, b = 200 and a = 100.
Therefore, we get 200 ft. as the length of the longest side.