SOLUTION: Why a lengths of 15 13 12 could represent the measure of the sides of a triangle

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Question 836596: Why a lengths of 15 13 12 could represent the measure of the sides of a triangle
Found 3 solutions by Alan3354, MathLover1, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

use this simple formula to figure it out:
let's a=15,+b=13,+c=12

if a%2Bb%3Ec, a%2Bc%3Eb, and b%2Bc%3Ea, than given lengths could represent the measure of the sides of a triangle
a%2Bb%3Ec => 15%2B13%3E12 =>28%3E12.............true
a%2Bc%3Eb=> 15%2B12%3E13 =>27%3E13.............true
b%2Bc%3Ea => 13%2B12%3E15 =>25%3E15.............true

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Given a triangle, the sum of any two side lengths must be strictly greater than the third side. In particular, we only need to check whether the sum of the shortest two sides is greater than the longest side (do you see why?).

Since 12 + 13 > 15, (12, 13, 15) could be the sides of a triangle.