A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 meters. Find the dimensions of the window to admit maximum light through the whole opening. How having large windows help us in saving electricity and conserving environment?

Question

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 meters. Find the dimensions of the window to admit maximum light through the whole opening. How having large windows help us in saving electricity and conserving environment?

Philoid · Accepted Answer

Given:

• Total perimeter of window = 10m

Let the dimension of the window be 2x and 2y as shown

Perimeter of window = 2x + 4y + πx = 10

Area,

we get maxima for as

For

So, the required dimensions are

Having large windows can help us in saving electricity in several ways. For example, we get proper light and air through the window which will definitely remove the need of bulb and fans thus saving electricity and hence saving the environment also.