Q24 of 45 Page 1

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximumarea.


Let the length of a rectangle be l and breadth be b and the radius of a circle is a and the diagonal’s length be 2a.


As per Pythagoras theorem,


(Hypotenuse)2 = (Perpendicular)2 + (Side)2


(2a)2= l2 + b2



Area of rectangle =



=






4a2 = 2l2




Using second derivative test,


l =


Then the area of rectangle is the maximum.


Since,


l = b = , the rectangle is a square.


Hence proved.


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