Question

The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 8 cm and a second side that is 4 cm less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

Good afternoon, 

First side= 8cm 
Third side= x
Second side= 2x-4

We know that the sume of the lenghts of any two sides must be greater than the third side, so:

$Second \,\,\,\,side+Third\,\,\,\,side>First\,\,\,\,side \\ 2x-4 + x >8 \\ 3x>12 \\ x>4$

Answer: Third side= x                        ;         where: x>4 or (4,+infinity)
                Second side= 2x-4              ;         where: x>4 or (4,+infinity)