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

Explanation:

Step1: Check Don's wires

Sum of two shorter sides: $3 + 5 = 8$. Compare to longest side ($12$): $8 < 12$ → No triangle.

Step2: Check Margo's wires

Sum of two shorter sides: $6 + 8 = 14$. Compare to longest side ($14$): $14 = 14$ → No triangle.

Step3: Check Sonji's wires

Sum of two shorter sides: $8 + 12 = 20$. Compare to longest side ($17$): $20 > 17$ → Triangle possible.

Step4: Check Liam's wires

Sum of two shorter sides: $8 + 16 = 24$. Compare to longest side ($27$): $24 < 27$ → No triangle.

Answer:

Sonji