Two sides of a triangle measure 14 and 10. If A is the set of possible lengths for the third side, how many elements of A are integers?

Question

Is the correct answer 19 elements of A are integers?

Answer 1

let the third side be x

The sum of any two sides must be greater than the third side

x+14 > 10 or
x > -4, but x must be positive, so x> 0 DUHH!

AND

x+10 > 14
x > 4

AND

10+14 > x
x < 14 --------> 4 < x < 14

so x has to be 5, 6, 7 , .... 13
I count 9