Posted by Mark on .
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?
Is the correct answer 19 elements of A are integers?

Math 
Reiny,
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