$\"\"$

The equation of the circle is $\"\"$ .

Where $\"\"$ is radius of the circle.

Therefore equation of semi circle is $\"\"$ .

The area of the rectangle is inscribed in the semi circle.

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .

Calculate the derivative of $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ is maximum when $\"\"$ .

$\"\"$

Therefore the dimensions are :

Length : $\"\"$ .

Width : $\"\"$ .

$\"\"$

Length of the rectangle is $\"\"$ .

Width of the rectangle is $\"\"$ .