Question

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.

Answer 1

The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.

Explanation:

Answer 2

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. 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.