SOLUTION: A triangle has two sides of length 19 and 19. What is the largest possible whole-number length for the third side?

Question 1202400: A triangle has two sides of length 19 and 19. What is the largest possible whole-number length for the third side?
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
The last side MUST BE SMALLER THAN 19+19=38 units.
Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.

        It is     19 + 19 - 1 = 37.         ANSWER

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

We are given a triangle with sides a = 19 and b = 19. This triangle is isosceles (or could be equilateral).

The third side c has the interval of:
b-a < c < b+a
19-19 < c < 19+19
0 < c < 38
Refer to the triangle inequality theorem for more information.

If c is a positive whole number, then we can select values from this set {1,2,3,...,35,36,37}

c = 1 is the smallest side possible
c = 37 is the largest side possible for that missing 3rd side.

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