Let the area of the rectangle ABCD be denoted by [tex]A_1[/tex].
Therefore, [tex]A_1=x\times 12=12x[/tex]........(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 [tex]A_2[/tex]
Therefore, [tex]A_2=16 \times (x-2)=16(x-2)=16x-32[/tex]....(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:
[tex]A_1=A_2[/tex]
Therefore, equating the two equations (Equation 1 and Equation 2) we get:
[tex]12x=16x-32[/tex]
[tex]12x-16x=-32[/tex]
[tex]-4x=-32[/tex]
[tex]x=\frac{-32}{-4}=8[/tex]
Thus, the value of x such that the rectangles have the same area is 8 meters.
