The Ladder Problem and Extension

This issue's problem comes from Ron Lancaster, of Saint Paul's School in Ontario, Canada. Ron presented this problem at the North Carolina School of Science and Mathematics' annual Teaching Contemporary Mathematics Conference last February. We had a wonderful time playing with Ron's problem and want to share it with the Consortium readers.

Downtown Toronto is filled with public art and interesting architecture and makes a wonderful location for a Math Trail. In one building, there are a series of ladders leaning against a wall. As part of the Math Trail, Ron posed the following problem to his students:

Walk over to one of the ladders that is leaning against the wall at an angle. If you were able to move this ladder at the base, so that it became 10 centimeters further from the wall, would the top of the ladder slide down the wall through a distance of 10 centimeters?

While the public art adds a unique flavor to the problem, it also works very well in the classroom context. It is surprising how quickly and confidently students answer the question Yes! Here is where the investigation begins.