What are the dimensions of the original figure?

Question

The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 324 square inches. What are the dimensions of the original figure?

Answer 1

Translate the words into algebra variables and operations:

The length (L) is 4 more than the width (W)           means      L = 4 + W

Now, the sides are modified.

      The length becomes   L -2   and the new width is   W + 2   and it is a square.

      The area of the square = 324, so the equal sides must be 18 and 18.

The original length is 20.

The original width is 16.

Note that L=16 and W=20 is not correct.  Explain why.