Question

Use the Triangle Inequality Theorem to determine which set of sides will form a triangle.





*Remember the sum of 2 sides must be GREATER than the 3rd remaining side.


A.
3, 4, 10

B.
4, 6, 12

C.
2, 5, 6

D.
2, 10, 15

Answer 1

To determine which set of sides will form a triangle using the Triangle Inequality Theorem, we need to check if the sum of any two sides is greater than the third side for each set.

**A.** 3, 4, 10
- 3 + 4 = 7 (not greater than 10)
- 3 + 10 = 13 (greater than 4)
- 4 + 10 = 14 (greater than 3)

Since 3 + 4 is not greater than 10, this set **cannot** form a triangle.

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**B.** 4, 6, 12
- 4 + 6 = 10 (not greater than 12)
- 4 + 12 = 16 (greater than 6)
- 6 + 12 = 18 (greater than 4)

Since 4 + 6 is not greater than 12, this set **cannot** form a triangle.

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**C.** 2, 5, 6
- 2 + 5 = 7 (greater than 6)
- 2 + 6 = 8 (greater than 5)
- 5 + 6 = 11 (greater than 2)

All conditions are satisfied, so this set **can** form a triangle.

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**D.** 2, 10, 15
- 2 + 10 = 12 (not greater than 15)
- 2 + 15 = 17 (greater than 10)
- 10 + 15 = 25 (greater than 2)

Since 2 + 10 is not greater than 15, this set **cannot** form a triangle.

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In conclusion, the only set of sides that can form a triangle is:

**C. 2, 5, 6**.