A window is in the form of rectangle surmounted by a semicircular opening The total perimeter of the window - Maths - Application of Derivatives

Question

A window is in the form of rectangle surmounted by a
semicircular opening The total perimeter of the window is 10 m Find
the dimensions of the window to admit maximum light through the
whole opening

Gopal Mohanty · Accepted Answer

Let x and y be the length and breadth of the rectangular window Radius of the semicircular opening

It is given that the perimeter of the window is 10 m

∴Area of the window (A) is given by,

Thus, when

Therefore, by second derivative test, the area is the maximum when length

Hence, the required dimensions of the window to admit maximum light is given by

A window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.