math league problem

Chuck Biehl (
Wed, 11 Dec 1996 05:40:12 -0500 (EST)

We have this problem that neither of us can figure out. I can't include
the diagram, so try to use your imagination.

Diagram: A scalene triangle with horizontal base. Vertices are labeled
clockwise from the bottom left as A, B, and C. Horizontal segments are
drawn in the triangle parallel to AC such that the altitude is divided
into 5 equal segments, making the triangle divided into 5 "strips" of
equal width. The second strip from the bottom is shaded.

The question: "What is the ratio of the shaded area to the unshaded area?"
The answer is given as 7/18, with an explanation that we cannot
understand. I won't share the explanation here so as to not spoil the fun.
Can somebody help us out?

L. Charles (Chuck) Biehl
The Charter School of Wilmington
Wilmington, DE 19807
(v)302.651.2727 (f)302.652.1246