Question
A rectangle is inscribed in a semi-circle of radius r with one of its sides on the diameter of the semi-circle. Find the dimensions of the rectangle so that its area is maximum Find also this area.
Solution
Let PQRS be the rectangle inscribed in the semi-circle of radius r so that OR = r, where O in centre of circle.
Let PO = OQ = x and QR = y so that sides of rectangle are of lengths 2x and y respectively.
Let
In
and
Let A be area of rectangle PQRS.
For A to be maximum or minimum
Let PO = OQ = x and QR = y so that sides of rectangle are of lengths 2x and y respectively.
Let
In
and
Let A be area of rectangle PQRS.
For A to be maximum or minimum
