Step-by-step explanation:
The Triangle Inequality Theorem states that any two sides of the triangle must add up to be greater than the third side.
<h3>Question #1</h3>
Here we have a triangle that has side lengths of 10 in, 11 in, and ? in.
This last side length must add up to 10 in to be greater than 11 in.
The least possible whole number that would fit this description would be 2 in.
- 10 in + 2 in > 11 in
- 10 in + 11 in > 2 in
- 11 in + 2 in > 10 in
The missing side length should be labeled as 2 inches.
<h3>Question #2</h3>
We are given a triangle with side lengths of 6 in and 8 in. We are asked to choose all answers that apply from this list:
- 2 in
- 3 in
- 4.5 in
- 6.5 in
- 10 in
- 13.5 in
- 14 in
- 15.5 in
We can tell that 2 in cannot be an answer since 6 in + 2 in is not greater than 8 in.
We also know that 14 in and 15.5 in cannot be part of the answer choices since 8 in + 6 in = 14 in, and this is not greater than 14 in or 15.5 in.
The rest of the answer choices will form a triangle if we follow the Triangle Inequality Theorem. You can test it out yourself to check.
Therefore, the answer choices are:
- B. 3 in
- C. 4.5 in
- D. 6.5 in
- E. 10 in
- F. 13.5 in
<h3>Question #3</h3>
We are given these possible side lengths:
Let's test out which combinations will create a triangle.
- 2 + 4 > 5
- 5 + 2 > 4
- 4 + 5 > 2
The straw lengths 2, 4, and 5 will form a triangle.
- 2 + 5 > 6
- 5 + 6 > 2
- 2 + 6 > 5
The straw lengths 2, 5, and 6 will form a triangle.
The straw lengths 2, 4, and 6 will NOT form a triangle.
- 4 + 5 > 6
- 6 + 5 > 4
- 4 + 6 > 5
The straw lengths 4, 5, and 6 will form a triangle.
- 5 + 6 > 10
- 10 + 5 > 6
- 6 + 10 > 5
The straw lengths 5, 6, and 10 will form a triangle.
We have no more straw lengths that will form a triangle, since adding up each remaining pair of given straw lengths do not output a value greater than another number.
