Length of a rectangular yard is 4 ft longer than its width w. the area of the yard is 525 ft2. (a) write a quadratic equation in terms of w that represents the situation. (1 point) (b) what are the dimensions of the yard? show your work. (2 points)

The answer is
(a) w² + 4w - 525 = 0
(b) length = 25 ft; width = 51 ft

length of a rectangular yard is 4 ft longer than its width w:
l = w + 4
 
The area of the yard is 525 ft2: A = 525 = l * w

(a) So:
l * w = 525
(w + 4) * w = 525
w² + 4w = 525
w² + 4w - 525 = 0

(b) Solve quadratic function:
w = (-b +/-√(b² - 4ac)/(2a)
    = (-4 +/-√(4² - 4 * 1 * (-525)))/(2*1)
    = (-4 +/-√(16 + 2100))/2
    = (-4 +/-√2116))/2
    = (-4 +/- 46)/2

w = (-4 - 46)/2 = -50/2 = -25       width cannot be negative, so w ≠ -25
or
w = (-4 + 46)/2 = 42/2 = 21

Since l = w + 4 and w = 21, then l = 21 + 4 = 25.