Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which of the following sets of side lengths, in inches, will form a triangle? A. 3.5, 7.2, and 3.0B. 3.2, 5.9, and 4.5C. 10.0, 4.6, and 5.3D. 5.5, 4.9, and 10.5

Sagot :

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.

View image AndrayaJ379775
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.