SOLUTION: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Question 1191537: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
unknown triangle side length x

Sum of any two sides must be larger than the other side.

Last inequality not useful.

The whole value between these two is 13.

~~Largest whole number, 11.~~
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side
~~~~~~~~~~~~~~~

The correct answer is 13.

The answer 11, given by @josgarithmetic, is INCORRECT.

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

a = 1 and b = 13 are the known sides of the triangle.
c is the missing side.

Due to the modified version of the triangle inequality theorem, we could say,
b-a < c < b+a
13-1 < c < 13+1
12 < c < 14

If c is restricted to whole numbers only, then c = 13 is the only possibility.

Answer: 13

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