Triangles Unit Test

Question

1 of 151 of 15 Items
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.

No, because two out of three conditions are met.
No, because two out of three conditions are met.

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.

Answer 1

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

Let’s check the conditions:

1. 3 + 4 > 5

   • 7 > 5 (True)

2. 3 + 5 > 4

   • 8 > 4 (True)

3. 4 + 5 > 3

   • 9 > 3 (True)

All three conditions are satisfied, so the sides can indeed form a triangle.

The correct response is: Yes, because the sum of any two sides is greater than the third side.