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Q. The maximum area of a rectangle that can be inscribed in a circle of radius $2$ units is (in square units)

KCETKCET 2008Application of Derivatives

Solution:

The maximum area of a rectangle that inscribed in a circle is equal to the area of square whose diagonal length is $4$ unit.
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Let the side of square be $x$ unit.
$\therefore \,\,\,\,(4)^{2}=x^{2}+x^{2}$
$\Rightarrow \,\,\,\,2 x^{2}=16$
$\Rightarrow \,\,\,\,\,x^{2}=8$ sq unit