Question

an artist is using pieces of yarn to create various triangular shapes. he measured various pieces and wants to determine if they can be used to create triangles. which lengths of yarn can be used to form the three sides of a triangle? use triangle inequality theorem. 1 inch, 2 inches, 3 inches 8 inches, 12 inches, 20 inches 6 inches, 9 inches, 2 inches 9 inches, 8 inches, 4 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 option 1

For side - lengths 1 inch, 2 inches, 3 inches: $1 + 2=3$, which does not satisfy the theorem since $1 + 2$ is not greater than 3.

Step3: Check option 2

For side - lengths 8 inches, 12 inches, 20 inches: $8+12 = 20$, which does not satisfy the theorem since $8 + 12$ is not greater than 20.

Step4: Check option 3

For side - lengths 6 inches, 9 inches, 2 inches: $6+2=8<9$, which does not satisfy the theorem since $6 + 2$ is not greater than 9.

Step5: Check option 4

For side - lengths 9 inches, 8 inches, 4 inches:
$9+8 = 17>4$; $9 + 4=13>8$; $8 + 4 = 12>9$. This set of side - lengths satisfies the Triangle Inequality Theorem.

Answer:

D. 9 inches, 8 inches, 4 inches