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State if the three numbers can be the measures of the sides of a triangle.
1) 12, 12, 12

2) 6, 11, 13

3) 11, 12, 16

4) 7, 8, 18

5) 6, 12, 21

6) 7, 10, 7

7) 8, 7, 1

8) 11, 22, 9

9) 10, 6, 3

10) 10, 19, 7

11) 6, 5, 6

12) 6, 3, 12

13) 7, 4, 6

14) 13, 7, 9

Respuesta :

DeanR

The triangle inequality says any two sides add up to more than the third side.  We only ever have to check that the two smaller sides are more than the biggest side.  

1) 12, 12, 12

YES.  

Sure, it's an equilateral triangle.

2) 6, 11, 13

6+11>13 YES

3) 11, 12, 16

11+12>16 YES

4) 7, 8, 18

7+8<18 NO

5) 6, 12, 21

6+12<21 NO

6) 7, 10, 7

7+7>10 YES

7) 8, 7, 1

1+7=8 That's called a degenerate triangle, vertices three collinear points.  A degenerate triangle is not a triangle.   NO

8) 11, 22, 9

9+11<22 NO

9) 10, 6, 3

3+6<10 NO

10) 10, 19, 7

10+7<19 NO

11) 6, 5, 6

5+6>6 YES

12) 6, 3, 12

6+3<12 NO

13) 7, 4, 6

4+6>7 YES

14) 13, 7, 9

7+9>13 YES

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