POTW #4 Answer and Explanation

This problem was possible, so any of you that said it was impossible was incorrect. As you can see from the picture to the right, the answer is l=16 and m=9.There is a very interesting way to get the answer. You could have done it algebraically or just use your geometry logic. The easiest way is to use your geometry logic.

You know (or hopefully you knew, because it said right in the problem) that this is a right triangle. In that case use pythagorean theorum and you get that the square root of 15^2 + 20^2 = the hypotenuse, which is 25. Now you know that l + m = 25. So then you get the area of the triangle to find the length of line BD. The base can be 15 and the height can be 20. (Note: to see this, you can picture out and rotate it, or you can simply turn your head or create a picture your brain.) You do 20*15*(1/2) and you get 150 for the triangle's area. Now, you use the other base, the hypotenuse and the height so that they equal 150. So 25*x*(1/2) = 150