Let's start by assigning variables to the dimensions of the rectangle. Let's say that the width is w meters, then the length is 2w - 2 meters (since the length is 2 m less than twice the width).
When 5 meters are added to the width, the resulting figure is a square with an area of 144 square meters. This means that the new width is w + 5 meters, and the new length is also w + 5 meters (since it's a square). We can write an equation for the area of this square:
(w + 5)^2 = 144
Simplifying the equation, we get:
w + 5 = 12
w = 7
Now that we know the width of the original rectangle, we can use the expression we came up with earlier for the length:
length = 2w - 2 = 2(7) - 2 = 12
Therefore, the dimensions of the original rectangle are 7 meters by 12 meters.