Wednesday, November 14, 2012

Inner triangle area

I haven't posted a puzzle for a long time.  So here's one.

I start with any old triangle.  I construct the three red lines shown above by the following:
1. Take one side of the triangle and divide it into thirds.
2. Draw a line from the one-third point to the opposite corner.
3. Repeat for the other sides of the triangle.  Make sure to pick the appropriate one-third point so that it resembles the above figure (which is to scale).

Find the ratio of the area of the pink inner triangle to the area of the large black triangle.  Prove it.

See the solution

1 comment:

miller said...

A little hint: There's a clever way to do it, and more brute force way to do it. The clever way involves center of mass.