Mathcounts Prep Site
Since my students (including my oldest son) are preparing for Mathcounts, I figured I’d post a link to a cool Mathcounts prep site: Elias Saab’s Mathcounts Drills.
This is a great source of practice problems for kids preparing for mathcounts, but also just a great source of problems in general.
So, I was trying a few for fun, and came across this one, which I thought was interesting and challenging: A triangle ABC has an area of 16 square centimeters. We extend the side AC to obtain a point M such that A is between M and C and AM=AC . We extend the side AB to obtain a point N such that B is between N and A and AB=BN . We extend the side BC to obtain a point P such that C is between P and B and BC=CP . How many square centimeters are in the area of the triangle MNP? (I don’t feel right about copying their image, so you’re going to have to draw your own diagram.)
With my rusty geometry and unsure how to approach the problem, I guessed that the area of the larger triangle might be four times that of the original triangle (just on a gut double the linears -> quadruple the area) but that isn’t right. So, let’s have some thoughts on how to solve this one. 🙂