Question

A triangle has two sides 14 and 3. What is the largest possible whole number length for the third side?
Please help! Thanks<:

Answer 1

16
Explanation

For every triangle whose sides are a, b, and c, these three inequalities
must hold:

a+b < c
a+c < b
b+c < a

So every triangle whose sides are 14, 3, and c, these three inequalities
must hold:

14+3 > c
14+c > 3
3+c > 14

These become

17 > c
c > -11 <--that will always hold!
c > 11

So 11 < c < 16

So the only values for the third side are between 11 and 17, exclusive.
That means the third side is either 13, 14, 15, or 16.

The largest possible whole number length is 16.