Multiple solutions

David Taub
This is an illustration of the multiple solutions to the problem mentioned in the my article in Nämnaren nr 1, 2015, page 35. Drag the slider to change proportions of the sides of the rectangle. Points P and E will automatically update to the correct locations. Every value of k between 1 and 2 represents a different solution to the problem, showing that the solution is far from unique. Here is the text of the original problem (which, for those who didn't read the article, contains a typo): Point P lies on segment BC on rectangle ABCD. Draw point E so that DE and AP are perpendicular to each other. IF AP = DE and the area of the rectangle is 900, find the length of AP and AD. Geogebra calculates and displays the relevant values for verification (for example, showing clearly that AP = DE in all cases). Note that these solutions assume that point E lies within the rectangle as implied by the original diagram that was included with the original problem with the typo. For k=1, point E coincides with point A. For k=2, point E coincides with the midpoint of BC.