Question 286089
Given:

A= 48cm²

W = L - 2

You know the area of a rectangle is A = W x L

Now, you can say:

48cm² = W x L

Substituting:

48cm² = (L - 2) L

You end up with a quadratic equation:

L² - 2L - 48 = 0

You can write this as:

L² - 8L + 6L - 48 = 0
(L² - 8L) + (6L - 48) = 0
L(L - 8) + 6 (L - 8) = 0
(L - 8)(L + 6) = 0
For this product to be true, one of them must be zero, so:

L - 8 = 0 ; L = 8
L + 6 = 0 ; L = -6  ** WE NEGLECT THE NEGATIVE ROOT.

Now that we have the length of the rectangle, we substitute this in  W = L - 2, and:

W = 8 - 6 = 2

w = 8 - 2 = 6