Cut The Cake, Please...
"Selling It" occasionally is a section in Consumer Reports, with a focus on the truthfulness of advertisements, often submitted by readers. Consider this claim posed in an advertisement...
It is possible to divide an 8-inch square cake into five square servings.
A Consumer Reports Editor replied: "You can divide a square cake into: five rectangles; two squares and three rectangles; three squares and two rectangles; four squares and one rectangle; even five triangles; but as a geometrically savvy reader points out, you'll be hard-pressed to get five squares from an 8 by 8 inch cake."
Then, three readers responded with three different "solutions" to back the advertiser's claim.
Your Task: Determine if the claim is True or False...which would include considering the possibility that some people claim it is possible and some do not.
Hint: Draw a square and start cutting....
Solution Commentary: The three solutions can be found on page 4 of the April, 1999, issue of Consumer Reports. Your reactions... I share one of the suggested solution below, represented in the form of a crocheted block:
Do you agree that this is a solution, as four of the people would have square pieces that have holes in them?
MJ (Bellingham) sent this solution: "Take 8 inch square. Mark off top edge 8/3" from right side, right side 8/3" from bottom, Bottom 8/3" from left and left 8/3" from top. Connect the marks for an interior square of side sqrt((8/3)2+(16/3)2). Cut that up into 4 equal squares. The remaining 4 rt triangles fit together into a square of side 16/3" Actually, none of the pieces are 'squares' since they have depth of however deep the cake it....The only other cake solution that immediately hit me, since they're not really squares anyway, is to slice the cake horizontally into 5 equal "squares."