An arched window formed from the union of a semicircle and a rectangle has total perimeter #540"cm"#. What is the maximum possible area of the window?
1 Answer
Maximum area is achieved when the bounding rectangle is a square of side
Explanation:
Let the length of the base of the rectangle be
Then the length of the perimeter of the semicircle is
The total perimeter of the window is
So
So
The area of the rectangle is
The area of the semicircle is
So the total area of the window is
This has maximum value when
The total height of the window is
Basically the maximum area is achieved when the bounding rectangle is a square of side