Question 657647
For a triangle, we know that the sum of the lengths of any two sides must be greater than the length of the third side.  
Based on that:
{{{x < 24 + 27}}}
{{{x < 51}}}
And
{{{x + 24 > 27}}}
{{{x > 3}}}
So,
{{{3 < x < 51}}}
The possible values for x range from 4 to 50.  There are 47 whole numbers in this range, so there are 47 different possible whole number values for x.