Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.

Accepted Solution

Let the two original dowels be of length x.
After cutting one of the dowels, the lengths will then be
x/2, x/2,x.

He cannot form a triangle using the three dowels because the triangle inequality requires that the sum of the two shorter sides of a triangle must be greater than the third side.Β  Here x/2+x/2=x equals the third side, so a triangle cannot be formed.

By the way, if he cuts the long dowel a little shorter, he will then be able to make a triangle.