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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}

1 Answer

11 votes

Answer:

{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

User Macbert
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