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A triangle has two sides of length 15 and 15. what is the largest possible whole number length for the third side 

User Joe Witt
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7 votes

Answer: 29

Work Shown

a = 15

b = 15

c = missing side

b-a < c < b+a ...... modification of the triangle inequality theorem

15-15 < c < 15+15

0 < c < 30

If c is a whole number, then the possible values for c are {1,2,3,..., 27,28,29}. In other words, c is between 1 and 29 inclusive.

The largest possible length for the third side is c = 29

c = 30 isn't possible because it results in a straight line rather than a triangle. This is why "or equal to" isn't involved with the inequality signs.

User Sznowicki
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