Which set of numbers could represent the lengths of the sides of a triangle. a)3,4,8 b)19,16,20 c)8,11,19 d)11,5,5 no guessing and show work you.

We can use the triangle inequality theorem to test each set of numbers. This theorem states that if the sides of a triangle are A, B, and C, then A+B>C, B+C>A, A+C>B. Otherwise, any two given sides must add to be greater then the third side.

A)

3+4>8

4+8>3

3+8>4

The second and third statements are false, therefore this cannot be a triangle.

B)

16+19>20

19+20>16

16+20>19

All of these statements are true, this can be a triangle.

C)

8+11>19

11+19>8

8+19>11

The first statement of this set is not true, therefore this set cannot be a triangle.

D)

11+5>5

5+5>11

11+5>5

The second statement of this set is not true, therefore this set cannot be a triangle.

From the calcuations above, its clear that the answer is B.

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