Triangles Unit Test

Question

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Question
Apply the Triangle Inequality Theorem to determine if sides with lengths of 3 feet, 4 feet, and 5 feet 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.
No, because two out of three conditions are met.

Answer 1

To determine if the sides with lengths of 3 feet, 4 feet, and 5 feet can form a triangle, we apply the Triangle Inequality Theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's evaluate the sides:

1. 3 + 4 > 5

   • 7 > 5 (True)

2. 3 + 5 > 4

   • 8 > 4 (True)

3. 4 + 5 > 3

   • 9 > 3 (True)

Since all three conditions are satisfied (the sum of any two sides is greater than the third side), the correct response is:

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