Lengthy Relationship Puzzle - Solution

x is 1

The sides of the triangle are 3, 5, 8.

Since 3 + 5 = 8, this triangle is "degenerate", i.e., it collapses into a straight line.

About 10% of the people catch this and conclude that x must be 0. But that's the wrong answer!

The right answer is that x=1, so the left most triangle is a degenerate 1, 4, 5 triangle, and the right most triangle is a degenerate 1, 3, 4 triangle.

(Nearly everyone gets this puzzle wrong!)

Submitted by Dave Grossman