Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 4 in., 5 in., and 1 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?

Question

Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 4 in., 5 in., and 1 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?

Yes, according to the Triangle Inequality Theorem
Yes, according to the Triangle Sum Theorem
No, according to the Triangle Inequality Theorem
No, according to the Triangle Sum Theorem

Answer 1

No, 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, 4 + 1 = 5, which is equal to the length of the third side. Therefore, Jeremiah will not be able to create a triangle with these lengths without modifying them.