Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
10, 20, 15
8, 8, 20
8, 4, 12
20, 10, 30
The set of side lengths that best satisfies the Triangle Inequality Theorem and can form a triangle is 10, 20, 15. Each pair of side lengths in this set satisfies the inequality condition.
To determine whether a triangle can be formed, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to each set of side lengths:
1) 10, 20, 15:
10 + 15 = 25 (greater than 20)
10 + 20 = 30 (greater than 15)
20 + 15 = 35 (greater than 10)
All the pairs of side lengths satisfy the inequality, so a triangle can be formed.
2) 8, 8, 20:
8 + 8 = 16 (smaller than 20)
8 + 20 = 28 (greater than 8)
8 + 20 = 28 (greater than 8)
Only the pair 8 + 20 satisfies the inequality, so a triangle can be formed.
3) 8, 4, 12:
8 + 4 = 12 (equal to 12)
8 + 12 = 20 (greater than 4)
4 + 12 = 16 (greater than 8)
Two out of three pairs satisfy the inequality, so a triangle can be formed.
4) 20, 10, 30:
20 + 10 = 30 (equal to 30)
20 + 30 = 50 (greater than 10)
10 + 30 = 40 (greater than 20)
Two out of three pairs satisfy the inequality, so a triangle can be formed.
In conclusion, three side lengths that form a triangle are:
10, 20, 15
8, 4, 12
20, 10, 30