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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?

Respuesta :

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Answer:

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.  

Step-by-step explanation:

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Ruben will not be able to make a triangle with his three pieces of wooden dowels because The sum of any two sides of the triangle will not always be greater than the third side.

Recall the triangle theorem :

  • The sum of any two sides of a triangle must be greater than the third side.

  • With two congruent dowels ; the length are the same ;
  • Cutting one of the two lengths into two to obtain 3 pieces.

  • Each dowel now represents a side of the triangle.

  • The sum of the cut dowel when added should be greater than the side in other to obey the triangle theorem.

However, this is impossible as the sum will be equal to the length of the third side.

  • Take the two congruent dowels as :
  • a = 10 ; b= 10
  • Cutting a into two Pieces ; say a = 6 ; c = 4

  • The sum of a + c should be greater than b (triangle theorem)
  • However, 6 + 4 = 10

Hence, since the three sides do not conform to the triangle theorem, then Ruben will not be able to make a triangle with the three pieces.

Learn more : https://brainly.com/question/19258025?referrer=searchResults

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