Apply the triangle inequality theorem to determine which three side lengths form a triangle.
A. 8, 4, 12
B. 8, 8, 16
C. 10, 20, 15
D. 20, 10, 30
To determine if three side lengths can form a triangle, we 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. For side lengths 8, 4, 12:
8 + 4 > 12 (TRUE)
8 + 12 > 4 (TRUE)
4 + 12 > 8 (TRUE)
Therefore, side lengths 8, 4, 12 can form a triangle.
B. For side lengths 8, 8, 16:
8 + 8 > 16 (FALSE)
Therefore, side lengths 8, 8, 16 cannot form a triangle.
C. For side lengths 10, 20, 15:
10 + 20 > 15 (TRUE)
10 + 15 > 20 (TRUE)
15 + 20 > 10 (TRUE)
Therefore, side lengths 10, 20, 15 can form a triangle.
D. For side lengths 20, 10, 30:
20 + 10 > 30 (FALSE)
Therefore, side lengths 20, 10, 30 cannot form a triangle.
Therefore, the side lengths that form a triangle are 8, 4, 12 and 10, 20, 15.