(a).

The width of the room is feet.

Since the rug will be feet from the edge of the room, the width of the rug is .

The length of the room is feet.

So the length of the rug is .

The area of the rug is .

.

Since the rug has to cover half area of the total floor the area of the rug should be sq.ft.

Therefore the equation to model the area of the rug in terms of is .

(b).

Now write the equation as a function of .

The function is  .

Draw the table to evaluate the equation for several values of .

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the points using a smooth curve.

(c).

Equation to model the area of the rug in terms of is .

Solve the equation .

If ,

The width of the rug is .

The length of the rug is .

The dimensions of the rug cannot be negative, hence they are not considered.

If ,

The width of the rug is .

The length of the rug is .

Therefore width of the rug is feet

Length of the rug is feet.

(a). The equation of the rug is .

(b).

Graph of the function is

(c).

Width of the rug is feet.

Length of the rug is feet.