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.
Let's apply this theorem to the given side lengths:
1. 8, 8, 20:
8 + 8 = 16 (which is less than 20)
8 + 20 = 28 (which is greater than 8)
8 + 20 = 28 (which is greater than 8)
Therefore, 8, 8, 20 do not form a triangle.
2. 8, 4, 12:
8 + 4 = 12 (which is equal to 12)
4 + 12 = 16 (which is greater than 8)
8 + 12 = 20 (which is greater than 4)
Therefore, 8, 4, 12 form a triangle.
3. 20, 10, 30:
20 + 10 = 30 (which is equal to 30)
10 + 30 = 40 (which is greater than 20)
20 + 30 = 50 (which is greater than 10)
Therefore, 20, 10, 30 also form a triangle.
4. 10, 20, 15:
10 + 20 = 30 (which is greater than 15)
20 + 15 = 35 (which is greater than 10)
10 + 15 = 25 (which is also greater than 20)
Therefore, 10, 20, 15 form a triangle.
In summary, the three side lengths that form a triangle are:
• 8, 4, 12
• 20, 10, 30
• 10, 20, 15
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
(1 point)
• 8, 8, 20
• 8, 4, 12
• 20, 10, 30
• 10, 20, 15
1 answer