Question

Which of the following sets of numbers could represent the three sides of a triangle?
{12,16,29}
{14,21,36}
{14,28,39}
{8,14,24}

Answer 1

Answer:

{14,28,39}

Step-by-step explanation:

By the Triangle Inequality Theorem, if given side lengths $a$, $b$, and $c$, where $c$ is the longest side of the triangle, then $a+b\geq c$ holds true.

For the first set of numbers, $12+16\ngeq29$, so it doesn't represent the three sides of a triangle

For the second set of numbers, $14+21\ngeq36$, so it doesn't represent the three sides of a triangle

For the third set of numbers, $14+28\geq39$, so it does represent the three sides of a triangle

For the fourth set of numbers, $8+14\ngeq24$, so it doesn't represent the three sides of a triangle