The first step to solve this problem is to represent
variables for the width and the length:
Let w = width of the rectangle
2w – 1 = length
of the rectangle
The formula to compute for the area of the rectangle is:
A = LW
Substituting the values and variables to the formula:
28 = w (2w – 1)
2w^2 – w = 28
2w^2 – w – 28 = 0
Solve the quadratic equation:
(2w + 7)(w – 4) = 0
w = -7/2 or w = 4
You cannot use the -7/2 because there is no negative
measurement.
W = 4 feet
L = 2(4) – 1 = 7 feet
Therefore the dimension of the rectangle is 4 feet by 7
feet.
