Answer
When x does not equal -2, l = 4x.
Work Step by Step
We are told that the area of the two rectangles is the same. This means we can set their areas equal to each other.
2x $\times$ (2x+4) = (x+2) $\times$ l
We then divide both sides by (x + 2) to get a rational expression.
l = (2x $\times$ (2x + 4)) $\div$ (x + 2)
We can then divide the top and bottom of the rational expression by (x + 2) to get l = 4x. We have to exclude x = -2 because if x equals -2, the denominator of the original rational expression would be 0, which is not correct.
l = 2x $\times$ 2 = 4x when x does not equal -2.
