Question

Based on the given segment lengths, determine whether the segments can form a triangle.

11.5,10.5, 6.1
9.5, 3.5, 4.5
8, 6.7, 1
8, 6.7, 9.8
5, 6, 8
9.5, 7.5, 8.5

Answer 1

Answer:

CAN form a triangle

1. 11.5,10.5, 6.1

4. 8, 6.7, 9.8

5. 5, 6, 8

6. 9.5, 7.5, 8.5

CAN NOT for a Triangle

2. 9.5, 3.5, 4.5

3. 8, 6.7, 1

Step-by-step explanation:

Answer 2

The segments of length (11.5, 10.5, 6.1), (8, 6.7, 9.8), (5, 6, 8), and (9.5, 7.5, 8.5) form a triangle as the sum of any two sides is always greater than the third side in these segments.

The segments of length (9.5, 3.5, 4.5), and (8, 6.7, 1) don't form a triangle as the sum of any two sides is not always greater than the third side in these segments.

What is the necessary condition to form a triangle?

The necessary condition for any three sides to form a triangle is that the sum of any two sides has to be greater than the third side.

How do we solve the given question?

In the question, we are given the lengths of the segments and asked whether the segments form a triangle or not.

We assess all the options for the necessary condition to check whether it's a triangle or not.

• 11.5, 10.5, 6.1: This is a triangle as the sum of any two sides is greater than the third side.
• 9.5, 3.5, 4.5: This is not a triangle as the sum of 3.5 and 4.5 is less than 9.5, that is, the sum of two sides is not greater than the third side.
• 8, 6.7, 1: This is not a triangle as the sum of 6.7 and 1 is less than 8, that is, the sum of two sides is not greater than the third side.

• 8, 6.7, 9.8: This is a triangle as the sum of any two sides is greater than the third side.
• 5, 6, 8: This is a triangle as the sum of any two sides is greater than the third side.
• 9.5, 7.5, 8.5: This is a triangle as the sum of any two sides is greater than the third side.

∴ The segments of length (11.5, 10.5, 6.1), (8, 6.7, 9.8), (5, 6, 8), and (9.5, 7.5, 8.5) form a triangle as the sum of any two sides is always greater than the third side in these segments.

The segments of length (9.5, 3.5, 4.5), and (8, 6.7, 1) don't form a triangle as the sum of any two sides is not always greater than the third side in these segments.

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