We have two variables and two equations:

- length * width = 52
- length = 4 * width - 3

Therefore we can plug one equation into the other to find the length and width:

- (4 * width - 3) * width = 52
- 4 * width
^{2}- 3 * width^{ }- 52 = 0

Using quadratic formula (-b ± √(b^{2}-4ac))/(2a):

- width = (3 ±√(3
^{2}-4(4)(-52)))/(2 * 4) - width = (3 ± 29)/8

Therefore width is either 4' or -3.25', but we take the positive value for lengths, so __width is 4'__

Plugging this back into equation 2 gives:

- length = 4 * (4) - 3

Therefore the **length is 13'**. Also plugging back into equation 1: 13 * 4 = 52 is satisfied