Increasing Rectangular Area

A farmer has a rectangular field that measures $120$ meters in length and $80$ meters in width. He wants to increase both the length and the width of his field by a uniform amount, $x$ meters, such that the new area of the field is $20 ext{ m}^2$ more than the original area. What is the value of $x$?

To solve for $x$, first determine the area of the original field and then set up the equation for the new area, considering the increased dimensions.