To determine if the three side lengths form a triangle, 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.
A. 20, 10, 30:
20 + 10 = 30 > 30 (true)
20 + 30 = 50 > 10 (true)
10 + 30 = 40 > 20 (true)
These side lengths form a triangle.
B. 10, 20, 15:
10 + 20 = 30 > 15 (true)
10 + 15 = 25 > 20 (true)
20 + 15 = 35 > 10 (true)
These side lengths form a triangle.
C. 8, 8, 20:
8 + 8 = 16 > 20 (false)
These side lengths do not form a triangle.
D. 8, 4, 12:
8 + 4 = 12 > 12 (false)
These side lengths do not form a triangle.
Therefore, options A and B form triangles, while options C and D do not.
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
A. 20, 10, 30
B. 10, 20, 15
C. 8, 8, 20
D. 8, 4, 12
3 answers
wrong. Given two sides a,b with a>b, then side c must satisfy
a-b < c < a+b
That means that only B forms a triangle.
a-b < c < a+b
That means that only B forms a triangle.
Apologies for the mistake in my previous response. Thank you for the correction.
To determine if a triangle can be formed with side lengths a, b, and c, where a > b:
The conditions for a triangle to be formed are:
a - b < c < a + b
Applying the conditions to the given side lengths:
A. 20, 10, 30:
20 - 10 = 10 < 30 and 30 < 20 + 10 = 30. The conditions are met, so a triangle can be formed.
B. 10, 20, 15:
20 - 10 = 10 < 15 and 15 < 10 + 20 = 30. The conditions are met, so a triangle can be formed.
C. 8, 8, 20:
8 - 8 = 0 < 20 but 20 is not less than 8 + 8 = 16. The conditions are not met, so a triangle cannot be formed.
D. 8, 4, 12:
8 - 4 = 4 < 12 but 12 is not less than 8 + 4 = 12. The conditions are not met, so a triangle cannot be formed.
Therefore, based on the Triangle Inequality Theorem, only option B (10, 20, 15) forms a triangle.
To determine if a triangle can be formed with side lengths a, b, and c, where a > b:
The conditions for a triangle to be formed are:
a - b < c < a + b
Applying the conditions to the given side lengths:
A. 20, 10, 30:
20 - 10 = 10 < 30 and 30 < 20 + 10 = 30. The conditions are met, so a triangle can be formed.
B. 10, 20, 15:
20 - 10 = 10 < 15 and 15 < 10 + 20 = 30. The conditions are met, so a triangle can be formed.
C. 8, 8, 20:
8 - 8 = 0 < 20 but 20 is not less than 8 + 8 = 16. The conditions are not met, so a triangle cannot be formed.
D. 8, 4, 12:
8 - 4 = 4 < 12 but 12 is not less than 8 + 4 = 12. The conditions are not met, so a triangle cannot be formed.
Therefore, based on the Triangle Inequality Theorem, only option B (10, 20, 15) forms a triangle.