Question

Which of the following sets of numbers could represent the three sides of a triangle? O {15, 27, 44} O {5,19,25} Submit Answer {10, 24, 33} O {6, 12, 19)

Answer 1

Explanation:

The inequality theorem states that the sum of any two sides of a triangle must be grater than the sum of the third side.

We have to try this rule for each option:

• {15, 27, 44}

$\begin{gathered} 27+44>15\rightarrow71>15\rightarrow\text{ true} \\ 27+15>44\rightarrow42>44\rightarrow\text{ false} \end{gathered}$

This cannot represent the sides of a triangle.

• {10, 24, 33}

$\begin{gathered} 10+24>33\rightarrow34>33\rightarrow\text{ true} \\ 10+33>24\rightarrow43>24\rightarrow\text{ true} \\ 33+24>10\rightarrow57>10\text{ }\rightarrow\text{ true} \end{gathered}$

This set can represent the sides of a triangle.

• {5, 19, 25}

$5+19>25\rightarrow24>25\rightarrow\text{ false}$

This set cannot represent the sides of a triangle.

• {6, 12, 19}

$6+12>19\rightarrow18>19\rightarrow\text{ false}$

This set cannot represent the sides of a triangle.

Answer:

The set of numbers that could reprensent the sides of a triangle is {10, 24, 33}