The area of a rectangle is 52 in². the length of the rectangle is 9 in. longer than the width. what is the width of the rectangle? 8 in. 6 in. 4 in. 3 in.

Length, l = width, w + 9
l = w + 9

area = length * width 
52 = l * w
52 = (w+9) w
52 = w^2 + 9w
w^2 + 9w - 52 = 0
w^2 + 13w - 4w - 52 = 0
w (w + 13) - 4 (w + 13) = 0
(w + 13) (w - 4) = 0

length = 13 in
width = 4 in