Question

For a craft project, four students each chose three pieces of wire from a box.

Don’s wires measure 3 inches, 5 inches, and 12 inches.
Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Liam’s wires measure 16 inches, 8 inches, and 27 inches.

Which student chose pieces that can be used to construct a triangle?

Don
Margo
Sonji
Liam

Answer 1

Sonji.

Check the triangle inequality (sum of the two shorter sides must exceed the longest):
- Don: 3+5=8 ≤ 12 → no
- Margo: 6+8=14 = 14 → degenerate, not a triangle
- Sonji: 8+12=20 > 17 → yes
- Liam: 8+16=24 < 27 → no