Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent
the sides of a triangle. Can you make a triangle with these three objects? Use the
Triangle Inequality Theorem explain why or why not.
Measurements of each object:
pencil #1: 7 inches
pencil #2: 6 inches
pencil #3: 6 inches
The three objects that could represent the sides of a triangle are pencil #1, pencil #2, and pencil #3. However, it is not possible to make a triangle with these three pencils using the Triangle Inequality Theorem.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, if we add the lengths of pencil #1 (7 inches) and pencil #2 (6 inches), it equals 13 inches, which is greater than the length of pencil #3 (6 inches).
However, if we add the lengths of pencil #1 (7 inches) and pencil #3 (6 inches), it equals 13 inches, which is equal to the length of pencil #2 (6 inches). This violates the Triangle Inequality Theorem, as the sum of the lengths of any two sides should be greater than the length of the third side.
Therefore, it is not possible to make a triangle with these three pencils.