Answer:
Thus the answer is A. 10 cm, 6 cm, 4 cm
Explanation:
Triangle Inequality Theorem
Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:
x + y > z
x + z > y
y + z > x
Combining the above inequalities, and provided y>z, the third size must satisfy:
y - z < x < y + z
The first combination y=6 cm z=4 cm produces the condition:
6 - 4 < x < 10
2 < x < 10
The third side is x=10 cm and it does not satisfy the inequality.
The rest of the combinations produce true inequalities:
B. 1 < x < 15 and x=9 satisfies the conditions
C. 1 < x < 9 and x=8 satisfies the conditions
D. 6 < x < 14 and x=10 satisfies the conditions
Thus the answer is A. 10 cm, 6 cm, 4 cm