(a)

The general form of the quadratic equation is .

Let the width of the rectangular shape of floor is w feet

Then its length(l ) is w + 14 feet.

The area of the rectangular shape of floor is 1632 square feet.

The area of the rectangle : .

Thus, = 1632.

Substitute corresponding values in above formula.

.

Thus, the quadratic equation for the area of the floor in terms of w is . 

(b)

The general form of quadratic equation is .

The quadratic formula  .

Find the length and width of the floor.

The quadratic equation is .

Apply distributive property : .

\ \

Subtract 1632 from each side. \ \

Apply additive inverse property: . \ \

Compare the above equation with general form.

.

Substitute the values of in quadratic formula.

\ \

\ \

and .

The value of dimension (width) is always positive, so consider value of w = 34 feet. 

If the width of the floor is w = 34 feet, then its length is w + 14 = 34+14 = 48 feet.

Thus,

Length of the floor is 48 feet.

Width of the floor is 34 feet

The quadratic equation for the area of the floor in terms of w is .

The width of the floor is 34 feet and its length is 48 feet.