The area of a rectangle is 65 ft2 , and the length of the rectangle is 3 ft less than double the width. find the dimensions of the rectangle.

Area = length x width
length = 2 x width - 3

i.e. 65 = w(2w - 3)
2w^2 - 3w - 65 = 0
(w + 5)(2w - 13) = 0
w = -5 or w = 6.5
but width cannot be negative, hence
width = 6.5 ft
Length = 2 x 6.5 - 3 = 13 - 3 = 10 ft