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:

To determine which student's wire lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Step 1: Check Don's wires (3, 5, 12)

• \(3 + 5 = 8\), and \(8 < 12\). So, Don's wires do not satisfy the triangle inequality.

Step 2: Check Margo's wires (6, 8, 14)

• \(6 + 8 = 14\), and \(14 = 14\) (not greater than 14). So, Margo's wires do not satisfy the triangle inequality.

Step 3: Check Sonji's wires (12, 8, 17)

• \(12 + 8 = 20\), and \(20 > 17\)
• \(12 + 17 = 29\), and \(29 > 8\)
• \(8 + 17 = 25\), and \(25 > 12\)

All three inequalities are satisfied, so Sonji's wires can form a triangle.

Step 4: Check Liam's wires (16, 8, 27)

• \(16 + 8 = 24\), and \(24 < 27\). So, Liam's wires do not satisfy the triangle inequality.

Answer:

Sonji