The width of a rectangle is 2m less than the length. the area is 48m squared. find the dimensions

Let the length = L
Then the width, W = L - 2

A = LW

48 = L(L - 2)

48 = L^2 - 2L

L^2 - 2L - 48 = 0

(L - 8)(L + 6) = 0

L - 8 = 0   or   L + 6 = -6

L = 8   or   L = -6

Since the length of a rectangle cannot be a negative number,
we discard the -6.

The length is 8m
The width is 2 m less than the length, so the width is 6 m.