Homework Help: Math

Posted by Mark on Monday, October 1, 2012 at 8:58pm.

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, Monday, October 1, 2012 at 9:20pm
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

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