Question

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

Answer 1

Let x and y be the dimensions of rectangle part of windows and x be side of equilateral part.

If A be the total area of window, then

[Differentiating with respect to x] 

Now, for maxima or minima,

i.e., for largest area of window, dimensions of rectangle are