To determine which three side lengths form a triangle, we can 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, 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)
None of these combinations satisfy the Triangle Inequality Theorem, so these side lengths do not form a triangle.
B. 8, 4, 12
4 + 8 = 12 (which is equal to 12)
4 + 12 = 16 (which is greater than 8)
8 + 12 = 20 (which is greater than 4)
These combinations satisfy the Triangle Inequality Theorem, so these side lengths form a triangle.
C. 20, 10, 30
10 + 10 = 20 (which is equal to 20)
10 + 30 = 40 (which is greater than 20)
20 + 30 = 50 (which is greater than 10)
These combinations satisfy the Triangle Inequality Theorem, so these side lengths form a triangle.
D. 10, 20, 15
10 + 20 = 30 (which is greater than 15)
10 + 15 = 25 (which is greater than 20)
15 + 20 = 35 (which is greater than 10)
These combinations satisfy the Triangle Inequality Theorem, so these side lengths form a triangle.
Therefore, the side lengths that form a triangle are B. 8, 4, 12; C. 20, 10, 30; and D. 10, 20, 15.
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
(1 point)
A. 8, 8, 20
B. 8, 4, 12
C. 20, 10, 30
D. 10, 20, 15
1 answer