2. The length of a rectangular floor is 4 ft longer than its width w. The area of the floor is 525 ft2. (a) Write a quadratic equation in terms of w that represents the situation. (b) What are the dimensions of the floor? Show your work.

The area of a rectangle is calculated by multiplying the dimensions (length and width). If we let the width be w, the length, which is 4 ft longer than the width will be represented as w+4.

(a) The quadratic equation that would best represent the given is,

(w) (w + 4) = 525

w² + 4w = 525 or w² + 4w - 525 = 0

(b) Solving for the values of w in the quadratic equation,

w = 21 and w = - 25

Thus, we take w as 21 and w+4 = 25. The dimensions of the floor are therefore 21ft and 25 ft.