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

{14,28,39}

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\\geq29`, so it doesn't represent the three sides of a triangle

For the second set of numbers,
`14+21\\geq36`, 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\\geq24`, so it doesn't represent the three sides of a triangle