To solve this problem we must use the Triangle Inequality Theorem, which says:
In mathematical terms, if the triangle has sides of length a, b and c, the theorem states:
[tex]\begin{gathered} a+b>c \\ b+c>a \\ c+a>b \end{gathered}[/tex]We will verify which of the options satisfies the inequalities above.
A)
10 + 12 > 3 ✓
12 + 3 > 10 ✓
3 + 10 > 12 ✓
B)
14 + 8 > 3 ✓
8 + 3 < 14 ✖
3 + 14 > 8 ✓
C)
15 + 5 > 9 ✓
5 + 9 < 14 ✖
9 + 14 > 5 ✓
Answer
We see that the only sets of lengths that satisfy the three inequalities of the Triangle Inequality Theorem are the ones from option A.
