Asked by Somebody

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



Answered by Somebody
20 + 10 > 30 ---> 30 > 30 (not a triangle)
20 + 30 > 10 ---> 50 > 10 (triangle)
10 + 30 > 20 ---> 40 > 20 (triangle)

its not a triangle but this is
. For sides 10, 20, 15:
10 + 20 > 15 ---> 30 > 15 (triangle)
10 + 15 > 20 ---> 25 > 20 (triangle)
20 + 15 > 10 ---> 35 > 10 (triangle)
Answered by GPT 3.5
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using this theorem:
1. For sides 8, 4, 12:
8 + 4 > 12 ---> 12 > 12 (not a triangle)
8 + 12 > 4 ---> 20 > 4 (triangle)
4 + 12 > 8 ---> 16 > 8 (triangle)

2. For sides 10, 20, 15:
10 + 20 > 15 ---> 30 > 15 (triangle)
10 + 15 > 20 ---> 25 > 20 (triangle)
20 + 15 > 10 ---> 35 > 10 (triangle)

3. For sides 20, 10, 30:
20 + 10 > 30 ---> 30 > 30 (not a triangle)
20 + 30 > 10 ---> 50 > 10 (triangle)
10 + 30 > 20 ---> 40 > 20 (triangle)

4. For sides 8, 8, 20:
8 + 8 > 20 ---> 16 > 20 (not a triangle)
8 + 20 > 8 ---> 28 > 8 (triangle)
8 + 20 > 8 ---> 28 > 8 (triangle)

Therefore, the three side lengths that form a triangle are: 10, 20, 15 and 20, 10, 30.
Answered by GPT 3.5
Apologies for the error in my response. You are correct. Thank you for pointing it out.

The three side lengths that form a triangle from the options provided are: 10, 20, 15.