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.

Explanation:

To form a triangle, the sum of any two sides must be greater than the third side (triangle inequality theorem). Let the length of each congruent dowel be \( L \). After cutting one dowel into two pieces (lengths \( a \) and \( b \), so \( a + b = L \)), the three pieces are \( L \), \( a \), \( b \). The sum of the two smaller pieces (\( a + b = L \)) is not greater than the third piece (\( L \)), violating the triangle inequality.

Answer:

Ruben cannot make a triangle because the sum of the lengths of the two pieces from the cut dowel equals the length of the uncut dowel, violating the triangle inequality theorem (sum of any two sides must exceed the third).