Question

for a craft project, four students each chose three pieces of wire from a box.
dons wires measure 3 inches, 5 inches, and 12 inches.
margos wires measure 6 inches, 8 inches, and 14 inches.
sonjis wires measure 12 inches, 8 inches, and 17 inches.
liams wires measure 16 inches, 8 inches, and 27 inches.
which student chose pieces that can be used to construct a triangle?

Explanation:

Step1: Check triangle inequality for Don

Check if \(3 + 5>12\). \(3+5 = 8<12\). So, Don's wires can't form a triangle.

Step2: Check triangle inequality for Margo

Check if \(6 + 8>14\). \(6 + 8=14
ot>14\). So, Margo's wires can't form a triangle.

Step3: Check triangle inequality for Sonji

Check \(12+8>17\), \(12 + 8=20>17\); \(12+17>8\), \(12 + 17 = 29>8\); \(8+17>12\), \(8+17=25>12\). So, Sonji's wires can form a triangle.

Step4: Check triangle inequality for Liam

Check if \(16+8>27\). \(16 + 8=24<27\). So, Liam's wires can't form a triangle.

Answer:

Sonji