Triangles Online Practice

Question

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Question
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 cm, 7 cm, and 8 cm form a triangle.(1 point)
Responses

Yes, because the sum of any two sides is greater than the third side.
Yes, because the sum of any two sides is greater than the third side.

Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is less than the third side.

No, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.

No, because two out of three conditions are met.

Answer 1

To determine whether the sides with lengths of 3 cm, 7 cm, and 8 cm form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any three lengths to form a triangle, the following conditions must be met:

1. The sum of the lengths of any two sides must be greater than the length of the third side.

Let's check each condition:

1. \(3 + 7 > 8\)

   • \(10 > 8\) (True)

2. \(3 + 8 > 7\)

   • \(11 > 7\) (True)

3. \(7 + 8 > 3\)

   • \(15 > 3\) (True)

Since all three conditions are true, the answer is:

Yes, because the sum of any two sides is greater than the third side.