$\"\"$

\

The perimeter of window is $\"\"$ .

\

The window is has a shape of rectangle and surmounted by an equilateral triangle.

\

Hence the perimeter is $\"\"$ .

\

Therefore area of window $\"\"$ = area of rectangle + area of equilateral trianle

\

Consider the length is $\"\"$ and width is $\"\"$ .

\

The area of rectangle is $\"\"$ and area of equilateral triangle is $\"\"$

\

The total area is $\"\"$ .

\

if $\"\"$ then $\"\"$ .

\

Substitute $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The equation for area is $\"\"$ .

\

$\"\"$

\

The equation for area is $\"\"$ .

\

The area of window maximum occurs at $\"\"$ .

\

$\"\"$ here $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitue $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The area is maximum at length is $\"\"$ and width is $\"\"$ .