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Hello, can you please explaing this...
WHEN 2 * GREATEST(A, B, C) >= (A + B + C)
Thank you in advance!
The general rule/condition for a valid triangle is that the longest side should be less than the sum of the two other sides:
longestSide < sumOfOtherSides (1)
longestSide < sumOfOtherSides
For example, if you have A, B, and C, where B is the longest side, then the condition B < (A+C) is true for a valid triangle, and false otherwise.
B < (A+C)
Now, the sum of all the sides of the triangle is (A+B+C). Given B is the longest side, if you want to get the sum of other sides, you have to remove B from the sum of all sides, thus (A+C) = (A+B+C) - (B) or in other words:
(A+C) = (A+B+C) - (B)
sumOfOtherSides = sumOfAllSides - longestSide (2)
sumOfOtherSides = sumOfAllSides - longestSide
With this in mind, the first inequation (1) can now be written as :
longestSide < sumOfAllSides - longestSide
which is equivalent to
longestSide + longestSide < sumOfAllSides
2 * longestSide < sumOfAllSides (3)
2 * longestSide < sumOfAllSides
So, a triangle is valid if and only if inequation (3) is true. If (3) is false, then we have 2 * longestSide >= sumOfAllSides. In MySQL and Oracle SQL, the GREATEST() function returns the greatest value of the guiven arguments. Hence, you have longestSide = GREATEST(A, B, C).
2 * longestSide >= sumOfAllSides
longestSide = GREATEST(A, B, C)
Everything above put together, the final formula to check if a triangle is NOT valid is :
2 * GREATEST(A, B, C) >= (A + B + C)
Hope my explanation was clear and detailed!
Thank you for sharing this information.