Equations
This problem can be stated as a two-variable system of equations, but we'll manage to use only one variable, set up as:
x = width of the rectangle
Since the length is 4 less than twice the width:
2x - 4 = length of the rectangle
The perimeter is given by:
P = 2w + 2l
Substituting:
P = 2(x) + 2(2x - 4)
We know this perimeter is 52 inches, thus:
2(x) + 2(2x - 4) = 52
Operating:
2x + 4x - 8 = 52
Adding 8:
2x + 4x = 52 + 8
Simplifying:
6x = 60
Dividing by 6:
x = 60 / 6 = 10
x = 10 <--- the width of the rectangle
2x - 4 = 2*10 - 4 = 20 - 4 = 16 <----the length of the rectangle
The dimensions are:
width = 10 inches
lengh = 16 inches