SOLUTION: Given a set of three numbers 4,5,7 how can i find out if these numbers can be the lengths of the sides of a triangle.?

Suppose you were walking from A to C. There are two ways you could get there.
1. You could go from A to B, and then go from B to C.
or
2. You could go straight from A to C  

Taking the straight line shortcut from A to C MUST be shorter than going 
around by B. So the distance from A straight to C must be less than the
total distance going around by B.   That is true for any
triangle.

It comes from the fact that the shortest distance between two 
points is always the straight line between them.

Three numbers can be the lengths of the sides of a triangle
if the longest length is less than the sum of the two shorter
lengths.

The smallest two numbers are 4 and 5.
Add them. 4+5
Get 9  
The longest side 7 is shorter than 9, (the distance going around by B).
Therefore 4,5,7 CAN be the lengths of the sides of a triangle.

[Note: 4,5,9 could not be the lengths of the sides of a triangle, because
9 is not less than 4+5.
 Neither could 4,5,10, because 10 is not less than 4+5.    

Edwin