UPSC 2014 CDS I Math Paper

A rectangle of maximum area that can be inscribed in a circle is a square.
Let the side of the square be x cm. In right ΔABC,
x2+x2=52=25
⇒2x2=25⇒x2=

25

2

=12.5
Therefore, maximum area of the rectangle = Area of the square=12.5cm2