To determine which three side lengths form a triangle, we must 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) 8, 4, 12
8 + 4 = 12, which is equal to 12. Since this condition is not met, the sides 8, 4, and 12 do not form a triangle.
B) 8, 8, 20
8 + 8 = 16, which is less than 20. This condition is met, so the sides 8, 8, and 20 form a triangle.
C) 10, 20, 15
10 + 15 = 25, which is greater than 20. 20 + 15 = 35, which is greater than 10. 10 + 20 = 30, which is greater than 15. This condition is met, so the sides 10, 20, and 15 form a triangle.
D) 20, 10, 30
20 + 10 = 30, which is equal to 30. Since this condition is not met, the sides 20, 10, and 30 do not form a triangle.
Therefore, the three side lengths that form a triangle are:
B) 8, 8, 20
C) 10, 20, 15
apply the triangle inequality theorem to determine which three side lengths form a triangle.
A 8,4,12
B 8, 8, 20.
C 10, 20, 15.
D 20, 10, 30.
1 answer