Conclude by giving your students these challenges:
The L shape below consists of two overlapping congruent rectangles. If the perimeter of the L shape is 40 cm, what can we say about the length and width of each rectangle?
Here's the solution: Let \(w\) be the width for one of the rectangles, and \(h\) the height, with \(w \gt h.\) By rearranging the line segments which form the boundary of the L shape, we can see it has perimeter \(4w.\) Thus, we know \(4w = 40\) and therefore \(w = 4.\) We can't say anything about \(h.\) If instead, \(w \lt h,\) then \(h = 4,\) and we can't say anything about \(w.\) If \(w = h,\) then we no longer have an L shape, but a square. Since the problem specifies an L shape, this can't be the case.
Note: This is the NRICH problem L-emental. I copied it because I wanted to provide a more detailed solution.