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 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 inequality theorem
yes, according to the triangle sum theorem
no, according to the triangle inequality theorem
no, according to the triangle sum theorem

Explanation:

Step1: Check triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let \(a = 2\), \(b=4\), \(c = 5\).

• \(a + b=2 + 4=6>5\)
• \(a + c=2+5 = 7>4\)
• \(b + c=4 + 5=9>2\)

Step2: Analyze triangle sum theorem

The triangle sum theorem states that the sum of the interior angles of a triangle is \(180^{\circ}\), which is not relevant to checking if three side - lengths can form a triangle.

Answer:

Yes, according to the Triangle Inequality Theorem.