Dividing the Land - May 23-27, 1994 Two contractors, Jamal and Jacob, are trying to divide up a piece of land. The land is an irregular quadrilateral. Jamal decides he might be able to get something out of this, because Jacob doesn't seem too good with areas. Jamal says, "Let's draw the line AC, with you getting triangle ABC and me getting triangle ACD." Now, even Jacob knew this wasn't a good deal. So then Jamal said, "What if we draw another diagonal, BD? If AC and BD meet at E, you get AED and BEC, and I get AEB and CED." Jacob pondered this for a while, and figured out that the sums of the areas still weren't equal. "But," Jamal said, "the product of the areas is equal!" Jacob was stumped, and didn't really understand, so he agreed to the deal because it sounded really impressive. Is Jamal's claim about the products true for all quadrilaterals? Is this a fair way to divide the land? Why or why not? Extra: Come up with a way to divide an irregular quadrilateral using only two segments so that the four regions can be shared equally. Correct solutions to the problem were submitted by: Susan Quan Grade 7, Masterman, Philadelphia Alan Schultz Grade 9, Steel Valley High School Gino Perrotte Grade 10, Shaler Area High School These folks got the initial part right, and decided that it wasn't fair, but didn't do the extra part (or did it but weren't right): Rob Gallagher and Ryan Ferchak Grade 9, Steel Valley High School, PA Susie Taylor and Valerie Stalter Grade 10, Shaler Area High School The following person got it all right, but is a college professor, so he gets his own listing :-) Robert Dawson Dept. of Math & Computing Science, St. Mary's University Next problem || Previous problem || Table of Contents || Forum Home Page