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? don margo sonji liam

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check Don's wires

$3 + 5=8<12$, so Don's wires cannot form a triangle.

Step3: Check Margo's wires

$6 + 8 = 14$, which does not satisfy the triangle - inequality theorem. So Margo's wires cannot form a triangle.

Step4: Check Sonji's wires

$8+12 = 20>17$, $8 + 17=25>12$, $12 + 17 = 29>8$. Sonji's wires can form a triangle.

Step5: Check Liam's wires

$8+16 = 24<27$, so Liam's wires cannot form a triangle.

Answer:

Sonji