Question

Which set of side lengths will form a triangle? All measurements are in feet.
A. 8,6,2
B. 3,3,6
C. 5,2,4
D. 4,1,6

Answer 1

To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. We will check each set of side lengths:

A. **8, 6, 2**
- 8 + 6 > 2 (14 > 2) ✔
- 8 + 2 > 6 (10 > 6) ✔
- 6 + 2 > 8 (8 > 8) ✖ (not valid)

B. **3, 3, 6**
- 3 + 3 > 6 (6 > 6) ✖ (not valid)
- 3 + 6 > 3 (9 > 3) ✔
- 3 + 6 > 3 (9 > 3) ✔

C. **5, 2, 4**
- 5 + 2 > 4 (7 > 4) ✔
- 5 + 4 > 2 (9 > 2) ✔
- 2 + 4 > 5 (6 > 5) ✔

D. **4, 1, 6**
- 4 + 1 > 6 (5 > 6) ✖ (not valid)
- 4 + 6 > 1 (10 > 1) ✔
- 1 + 6 > 4 (7 > 4) ✔

The only set that satisfies the triangle inequality theorem is:

**C. 5, 2, 4**

Thus, option C can form a triangle.