Consider the sides of the rectangles be $\"\"$ and $\"\"$ .

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

Perimeter of the rectangle is $\"\"$ m.

Hence $\"\"$

$\"\"$

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

$\"\"$

Area of the rectangle is large when its first derivative becomes zero.

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

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Therefore the dimension of the rectangle is $\"\"$ m by $\"\"$ m.

The dimension of the rectangle is $\"\"$ m by $\"\"$ m.