Question

A large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.

Answer 1

Suppose the dimensions of the rectangle be x and y.

So, perimeter of the window = x + y + x + x + y = 12

3x + 3y = 12

y = (12 - 3x)/2 ...(1)

The area of the window 

For the maximum and minimum values of A, we must have

Hence, the area is maximum when