# Which one of the following sets of numbers could represent the lengths of the sides of a triangle? (a) (8,11,19) (b) (19,16,20), (c) (11,5,5) , (d) 13,4,8)?

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Dec 16, 2016

$\left(b\right) \left(19 , 16 , 20\right)$

#### Explanation:

The sum of the lengths of any two sides of a triangle must be greater than the third side.

$\left(a\right) \left(8 , 11 , 19\right) \implies 8 + 11$ not greater than $19$, (N.G.)
$\left(b\right) \left(19 , 16 , 20\right) \implies 19 + 16 > 20 , 19 + 20 > 16 , 16 + 20 > 19$, (OK)
$\left(c\right) \left(11 , 5 , 5\right) \implies 5 + 5 < 11$, (NG)
$\left(d\right) \left(13 , 4 , 8\right) \implies 4 + 8 < 13$, (NG).

Hence, option $\left(b\right)$ is the only answer.

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