$\"\"$

\

(a).

\

The perimeter of rectangular is $\"\"$ .

\

Consider length of rectangular is $\"\"$ and width of the rectangular is $\"\"$ ,Then perimeter of rectangular is $\"\"$ .

\

The area of rectangle $\"\"$ is $\"\"$ .

\

If $\"\"$ then $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

The area of rectangle as a fucntion of length $\"\"$ is $\"\"$ .

\

$\"\"$

\

(b).

\

Find the area of rectangle when width is maximum.

\

$\"\"$ is in the form of general quadratic equation.

\

Therefore $\"\"$ and $\"\"$ .

\

The maximum area occurs at $\"\"$ .

\

$\"\"$

\

The maximum width is $\"\"$ .

\

$\"\"$

\

(c).

\

Find the maximum area.

\

Substitute $\"\"$ in the function $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The maximum area is $\"\"$ .

\

$\"\"$

\

(a). $\"\"$ .

\

(b).The maximum width is $\"\"$ .

\

(c).The maximum area is $\"\"$ .