Consider all rectangles lying in the region (x, y) R R : 0 x 2 and 0 y 2 (2x) and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

JEE Advanced 2020 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2020

Consider all rectangles lying in the region

{(x, y) × : 0 x \ and\ 0 y 2(2x)}

and having one side on the -axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

(A)
(B)
(C)Correct
(D)

Answer: (C)

Solution

The curve is symmetric about . For the best rectangle the upper vertices lie on the curve; let its base extend from to , so width and height . Perimeter $p(x) =

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-033773