Question

the lenghts of two sides of. a triangle are 12cm and 15cm.between what two measures should be the length of the third side fall?with steps

Answer 1

by Pythagoras we have the min limit of third side as 
Let the length of third side be L
$15-12$ = 3 cm 

and we know the sum of any two sides > the third side so 12 + 15 = 27 cm 

so the third side ( L) must lie between 

3 < L < 27 cm

Answer 2

a triangle  ABC has 3 sides and they have to satisfy the following.
 
     | a - b |  <  c < (a+b) 
 length of a side must be less the sum of the other two and more than the difference between the other two.

Hence,  the third side,  has to be more than  (15-12) = 3 cm.   Also it has to be less than (15+12) = 27 cm.     It is in between  3 cm and 27 cm.