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

Let us use the Pythagorean theorem in identifying what triangle can be formed.

Let us assume that the 2 wooden dowels each measure 8 inches. We cut off one wooden dowel into half, so it becomes 2 pcs of 4 inches each.

The 3 wooden dowels now measure, 4 inches, 4 inches, and 8 inches. 

The Pythagorean theorem states: 

a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64

The measure of the cut wooden dowel must be longer than the uncut wooden dowel to create a triangle. 

I also tried this on a piece of paper, I cut each piece according to the assumed measure. No triangle can be formed under this activity. 

Answer 2

It is given in the question that

Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle.

First we have to check out triangle inequality theorem, which is sum of two sides of a triangle must be greater then the third side .

But here the sum of two pieces of the cutted dowel is equal to the lenth of the first dowel.

SO here triangle inequality theorem is not following .

Hence , Ruben will not be able to make a triangle with his three pieces.