106k views
8 votes
Which of the following sets of numbers could represent the three sides of a triangle?

Which of the following sets of numbers could represent the three sides of a triangle-example-1

1 Answer

6 votes

Answer:

5, 15, 19}

According to the triangle i

nequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.

Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:

a + b > c

b + c > a

a + c > b

Where a and b are the smaller side lengths, and c is the length of the longest side.

Let's check each set of numbers given to see if any satisfies this condition.

✍️Option 1: {6, 20, 28}

6 + 20 is not greater than 28

20 + 28 > 6

6 + 28 > 20

❌This set of numbers does not represent the sides of a ∆.

✍️Option 2: {4, 11, 15}

4 + 11 = 15

11 + 15 > 4

4 + 15 > 11

❌This set of numbers does not represent the sides of a ∆.

Option 3: {9, 19, 30}

9 + 19 is not greater than 30

19 + 30 > 9

9 + 30 > 19

❌This set of numbers does not represent the sides of a ∆

Option 4: {5, 15, 19}

5 + 15 > 19

15 + 19 > 5

5 + 19 > 15

✅This set of numbers does not represent the sides of a ∆

Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.

Explanation:

User Kamlesh Gallani
by
7.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories