Question

question 4 (multiple choice worth 4 points) (02.04r mc) 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 5 in, 5 in, and 2 in. will he be able to create the triangular component with these toothpicks without modifying any of the lengths? yes, according to the triangle sum theorem yes, according to the triangle inequality theorem no, according to the triangle sum theorem no, according to the triangle inequality theorem

Explanation:

Step1: Recall Triangle Inequality

For lengths $a,b,c$, sum of any two sides must be greater than the third side.

Step2: Test the given lengths

Let $a=5$, $b=5$, $c=2$.

• $5+5>2$ → $10>2$ (True)
• $5+2>5$ → $7>5$ (True)
• $5+2>5$ → $7>5$ (True)

Step3: Conclude validity

All conditions are satisfied, so a triangle can be formed.

Answer:

Yes, according to the Triangle Inequality Theorem