Question

Which of the following sets of numbers could represent the three sides of a triangle?

{6,18,24}
{5,16,22}
{11, 17, 27}
{ 8, 15, 24}

Answer 1

Answer: Choice C

{11, 17, 27}

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Step-by-step explanation:

Let's go through the answer choices.

• A) This won't work because 6+18 = 24 which is not larger than the third side 24. The sum of any two sides must be larger than the other side. Refer to the triangle inequality theorem.
• B) 5+16 = 21 is not larger than 22, so we rule this out as well.
• C) We'll come back to this later
• D) We rule this out because 8+15 = 23 is not larger than 24.

Now return back to choice C. Notice how adding any two sides leads to a sum larger than the third side

• 11+17 = 28 is larger than 27
• 11+27 = 38 is larger than 17
• 17+27 = 44 is larger than 11

The three conditions of the triangle inequality theorem are met, so a triangle is possible for choice C.