Question

Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses

8, 4, 12
8, 4, 12

10, 20, 15
10, 20, 15

20, 10, 30
20, 10, 30

8, 8, 20
8, 8, 20
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Answer 1

To determine which set of side lengths can form a triangle, we'll apply the Triangle Inequality Theorem. The theorem states that for any three sides $a$, $b$, and $c$ of a triangle, the following must be true:

1. $a+b>c$
2. $a+c>b$
3. $b+c>a$

Let's evaluate each set of side lengths:

1. 8, 4, 12

   • $8+4=12$ (not greater, so fails)
   • $8+12>4$ (true)
   • $4+12>8$ (true)
   • Does not form a triangle.

2. 10, 20, 15

   • $10+20=30>15$ (true)
   • $10+15=25>20$ (true)
   • $20+15=35>10$ (true)
   • Forms a triangle.

3. 20, 10, 30

   • $20+10=30$ (not greater, so fails)
   • $20+30>10$ (true)
   • $10+30>20$ (true)
   • Does not form a triangle.

4. 8, 8, 20

   • $8+8=16<20$ (not greater, so fails)
   • $8+20>8$ (true)
   • $8+20>8$ (true)
   • Does not form a triangle.

Conclusion: The only set of side lengths that can form a triangle is 10, 20, 15.