Which of the following sets of numbers could represent the three sides of a triangle? \{6,14,17\}{6,14,17} \{10,23,34\}{10,23,34

Question

2 years ago

10

} \{10,14,26\}{10,14,26} \{7,20,28\}{7,20,28}

1 answer:

abruzzese [7] · Answer 1 · 2023-02-27T15:52:45+03:00

The sets of numbers which could represent the three sides of a triangle is {6,14,17}. Option A is the correct option.

<h3>What is triangle inequality theorem?</h3>

Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus, according to this theorem,

$(a+b) > c\\(b+c) > a\\(c+a) > b$

The sides of first option are, 6,14,and 17.

$6+14 > 17\\20 > 17$

This set satisfy the triangle inequality theorem. All the other options do not follow, to satisfy this theorem.

Thus, the sets of numbers which could represent the three sides of a triangle is {6,14,17}. Option A is the correct option.

Learn more about the triangle inequality theorem here;

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