Answer :
We are given that the sum of the lengths of any two sides of a triangle must be greater than the third side
To find the possible lengths for the second and third sides, we will make an assumption below.
Let the third side be x
Since the second side is 2 cm less than twice the third side, this can be expressed as
[tex]\text{side 2=2x-2}[/tex]With this we can note that
side 1 = 16cm
side 2 =2x-2
side 3 = x
Going back to the initial rule that the sum of the lengths of any two sides of a triangle must be greater than the third side
We can sum any two sides and equate it to the third side.
[tex]\begin{gathered} \text{side}2+\text{side}3\text{ >side1} \\ 2x-2+x>16 \\ 3x>16+2 \\ 3x>18 \\ x>\frac{18}{3} \\ x>6 \end{gathered}[/tex]Since the third side is x therefore, the possible length of the third side is 6cm and above
ANSWER 1: third side= 7cm and above
Also, the second side is 2x-2. We will use a minimum value of 6
[tex]\begin{gathered} \text{side 2 = 2x-2} \\ \text{side 2 = 2(}6\text{)}-2 \\ \text{side 2 =12-2} \\ \text{side 2 =10} \\ \\ \end{gathered}[/tex]ANSWER 2: the second side is 10cm and above
