Q. 18 3.7( 7 Votes )

A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimensions of the rectangle so that its area is maximum. Find also the area.

Answer :

Let the length and breadth of rectangle ABCD be 2x and y respectively

Radius of semicircle = r (given)

In triangle OBA

r2 = x2 + y2 (Pythagoras theorem)

y2 = r2 - x2


Let us say, area of rectangle = A =xy

A = x () (from equation 1)

Condition for maxima and minima is

r2 – x2 = x2

2x2 = r2

x =

Since, x cannot be negative


For , < 0

A will be maximum for

From equation 1

y = =

Length of rectangle =

Breadth of rectangle =

Area of rectangle =

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