Question

Which set of the side lengths will form a triangle?
A. 3,4,6
B. 8,6,2
C. 5,2,3
D. 4,1,6

Answer 1

To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's evaluate each set of side lengths:

A. **3, 4, 6**
- \(3 + 4 = 7 > 6\) (Satisfied)
- \(3 + 6 = 9 > 4\) (Satisfied)
- \(4 + 6 = 10 > 3\) (Satisfied)
- This set can form a triangle.

B. **8, 6, 2**
- \(8 + 6 = 14 > 2\) (Satisfied)
- \(8 + 2 = 10 > 6\) (Satisfied)
- \(6 + 2 = 8 \not> 8\) (Not satisfied)
- This set cannot form a triangle.

C. **5, 2, 3**
- \(5 + 2 = 7 > 3\) (Satisfied)
- \(5 + 3 = 8 > 2\) (Satisfied)
- \(2 + 3 = 5 \not> 5\) (Not satisfied)
- This set cannot form a triangle.

D. **4, 1, 6**
- \(4 + 1 = 5 < 6\) (Not satisfied)
- This set cannot form a triangle.

Based on the evaluations, the only set of side lengths that can form a triangle is **A. 3, 4, 6**.