(August 14, 2016 at 7:41 am)Whateverist Wrote: Interestingly the area in red would be equal no matter where you draw the line so as to cut the rectangle in half through its center point. It would obviously be so for a line dividing the rectangle in two 10 by 10 squares or a line parallel to the two long sides bisecting the rectangle into two rectangles with the same length but half its height. But draw a line which goes through a point on the upper long side three units from the top left corner which connects to a point on the bottom long side three units from the bottom right corner, and the answer will still be the same.
This reminds me of a similar but harder middle school math problem. Five people wish to share a cake equally so that each one gets an equal portion of both cake and frosting. The cake has a square base and is a rectangular prism in shape. It is frosted (uniformly) only on the top and four sides above the platter on which it sits. Using only the minimum number of straight cuts made with a knife, explain how this can be done. (I always found more students would be successful if I specified a convenient side length for the cake, but it isn't necessary. A suggested side length is given below.)
I'm going to move this to its own thread to share it out more widely.
