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
===============================
Cheers,
Stan H.
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.
(
