Question 707256
The perimeter of the original triangle is 5+6+10 = 21


If you multiply this perimeter by 3 you get 3*21 = 63. If you don't know that 3*21 = 63, then you can see that 63/21 = 3. 


Apply this same scaling to each side to get 5*3 = 15, 6*3 = 18, 10*3 = 30


So the similar triangle with side lengths 15, 18, 30 is a triangle that has a perimeter of 63.


The shortest side is therefore <font color="red">15</font>