According to the triangle inequalities rule, the sum of any 2 sides has to be greater than that of the the third side.
We can write two inequalities to resemble this problem.
x + 15 > 19 and 15 + 19 > x
Now, solve for x for both inequalities.
Steps to solve:
x + 15 > 19
~Subtract 15 to both sides
x + 15 - 15 > 19 - 15
~Simplify
x > 4
Steps to solve:
15 + 19 > x
~Simplify
34 > x
We can put both inequalities together to get:
4 < x < 34
The only value from the list of options that can be "x" is 6.
Therefore, the answer is 6cm (Option A)
Best of Luck!
