A large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 2 metres find the dimensions of the rectangle that will produce the largest area of the window.

Explanation

Let the 2 sides be x,y

Given perimeter =2

P=3x+2y=2

y= `(2−3x)/2`

​area of the window is given by,

A=`xy+ sqrt3/4 x^2`

A=`(x(( 2−3x))/(2))​ + sqrt3/4​ x^2`

A=`x− 3/2​ x^2 + sqrt3/4 x^ 2`
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