Question

which set of side lengths can form a triangle? 1 inch, 9 inches, 12 inches 2 inches, 7 inches, 10 inches 3 inches, 8 inches, 10 inches 4 inches, 6 inches, 12 inches

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 the first set (1, 9, 12)

$1 + 9=10<12$, so it cannot form a triangle.

Step3: Check the second set (2, 7, 10)

$2 + 7 = 9<10$, so it cannot form a triangle.

Step4: Check the third set (3, 8, 10)

$3+8 = 11>10$, $3 + 10=13>8$, $8 + 10 = 18>3$, so it can form a triangle.

Step5: Check the fourth set (4, 6, 12)

$4+6 = 10<12$, so it cannot form a triangle.

Answer:

3 inches, 8 inches, 10 inches