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}

Question

asked Oct 24, 2023 173k views

1 Answer

Pezhman Parsaee · Answer 1 · 2023-10-30T15:16:58+0000

{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

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