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In order to see which sides form a triangle, we can apply the triangle inequality theorem:
Case A.
In this case, we can choose a=3.5, b=7.2 and c=3. By applying the inequalities, we get
[tex]\begin{gathered} 3.5+7.2>3\Rightarrow10.7>3\text{ Thats correct } \\ 3.5+3>7.2\Rightarrow6.5>7.2\text{ thats incorrect !} \end{gathered}[/tex]Then, these segments doesnt form a triangle.
Case B.
In this case, we can choose a=3.2, b=5.9 and c=4.5. By applying the inequalities, we get
[tex]\begin{gathered} 3.2+5.9>3\Rightarrow9.1>3\text{ Thats correct } \\ 3.2+4.5>5.9\Rightarrow7.7>5.9\text{ Thats correct } \\ 5.9+4.5>3.2\Rightarrow10.2>3.2\text{ Thats correct } \end{gathered}[/tex]Then, these segments can make a triangle
Case C.
In this case, we can choose a=10, b=4.6 and c=5.3. By applying the inequalities, we get
[tex]\begin{gathered} 10+4.6>5.3\Rightarrow14.6>5.3\text{ Thats correct } \\ 10+5.3>4.6\Rightarrow15.3>4.6\text{ Thats correct } \\ 4.6+5.3>10\Rightarrow9.9>10\text{ Thats incorrect } \end{gathered}[/tex]Then, these segments doesnt form a triangle.
Case D.
In this case, we can choose a=5.5, b=4.9and c=10.5. By applying the inequalities, we get
[tex]5.5+4.9>10.5\Rightarrow10.4>10.5\text{ Thats incorrect }[/tex]Then, these segments doesnt form a triangle.
Therefore, the answer is option B.
