You have two rectangles, rectangle abcd and efgh. the length of ab is x meters. the length of cd is 12 meters. the length of ef is 16 meters. the length of fg is x - 2 meters. you want to find the value of x so that the rectangles have the same area.

Let the area of the rectangle ABCD be denoted by .

Therefore, ........(Equation 1) [Reason: Area of any rectangle is the product of it's length and breadth]

Likewise, let the area of the rectangle EFGH be denoted by

Therefore, ....(Equation 2) [Reason: Area of any rectangle is the product of it's length and breadth]

Since the area of the two rectangles are equal, we will have:

Therefore, equating the two equations (Equation 1 and Equation 2) we get:

Thus, the value of x such that the rectangles have the same area is 8 meters.