Question 211911: Can you create a triangle with the following measurements: 6", 5" and 12"? What rule can you discover about the sides of a triangle?
I tried drawing a triangle with these measurements and have determined that it is not possible. Having trouble explaining what the rule would be.
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Rule; The sum of each pair of sides must be greater than
the length of the third side.
Your Case:
6 + 5 is not greater than 12
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Cheers,
Stan H.
Answer by MathTherapy(10559)  (Show Source):
You can put this solution on YOUR website! A triangle can ONLY be possible if the DIFFERENCE between 2 of its sides is greater than the 3rd side, AND ALSO less than their sum.
In this case, 6, 5, and 12:
Let's take the 2 sides, 6 & 5. The 3rd side, 12, is supposed to be greater than the other 2 sides' difference of 1, which IT IS (12 > 6 - 5). Therefore, this is okay. However, the 3rd side, 12, is ALSO supposed to be less than the sum of the other 2 sides, which IT IS NOT. In other words, 12 should be less than (6 + 5), but is not. Instead, 12 > (6 + 5).
Let's now try the 2 sides, 5 & 12. The 3rd side, 6, is supposed to be greater than the other 2 sides' difference of 7, which IT IS NOT (6 not > 12 - 5). However, the 3rd side, 6, is ALSO supposed to be less than the sum of the other 2 sides, which IT IS. In other words, (6 < 12 + 5).
As seen, 1 of the rules does apply in all cases, but BOTH NEVER APPLY. BOTH need to apply in order for a triangle to be constructed with the given sides.
If you should take any other 2 sides and apply the same rules, both rules WILL NOT BE SATISFIED. Therefore, a triangle with sides 5, 6, and 12 IS NOT POSSIBLE.
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