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?
A- Yes, according to the Tnangle Inequality Theorem
B- Yes, according to the Triangle Sum Theorem
C- No, according to the Tiangle Inequality Theorem
D- No, according to the Triangle Sum Theorem

The Triangle Inequality Theorem states that in a triangle, the sum of lengths any two sides must be greater-than the length of the third side. If not, it is not possible to create a triangle with those sides

Let's check out this for the given problem
If it is possible to create a triangle with the toothpicks of sides 4, 5 and 2 in then the triangle will have sides of length 4, 5, and 2 in

Let's see if these sides obey the Triangle Inequality Theorem

4 + 5 = 9 > 2
5 + 2 = 7 > 4
2 + 4 = 6 > 5

Hence these sides follow the Triangle Inequality Theorem and it is possible to create a triangle with those toothpicks

lumei lumei · Answer 2 · 2024-03-04T05:58:21+01:00

C- No, according to the Triangle Inequality Theorem

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, it is not possible to form a triangle with those side lengths.

Let's check this with the given toothpicks:

Toothpick lengths: 4 in, 5 in, and 2 in.

According to the Triangle Inequality Theorem:

1. 4 + 5 should be greater than 2
2. 4 + 2 should be greater than 5
3. 5 + 2 should be greater than 4

The first and the third conditions are satisfied:

1. 4 + 5 = 9, which is greater than 2
3. 5 + 2 = 7, which is greater than 4

However, the second condition is not satisfied:

2. 4 + 2 = 6, which is not greater than 5

Because one of the conditions is not satisfied, Jeremiah would not be able to create a triangle with toothpicks of lengths 4 in, 5 in, and 2 in without modifying any of the lengths.