Let's denote the width of the rectangle by W.
From the problem, we know that the length of the rectangle is 4 meters less than 2 times the width, or:
L = 2W - 4
We also know that the perimeter of a rectangle is given by:
P = 2L + 2W
Substituting the expression for L into the perimeter equation, we get:
P = 2(2W - 4) + 2W
P = 4W - 8 + 2W
P = 6W - 8
We are given that the perimeter is 34 meters, so we can set P equal to 34 and solve for W:
34 = 6W - 8
42 = 6W
W = 7
Therefore, the width of the rectangle is 7 meters.