Answer: The answer is x = 19.
Step-by-step explanation: Given that a flower pot has a base with six equal sides of measurement (x - 6) units. We are to find the value of the unknown quantity 'x' if the perimeter of the base is 78 units.
We know that the perimeter of a polygon is given by the sum of the lengths of all the sides of the polygon.
Since each side of the six-sided base is (x - 6) units, so its perimeter will be
![6\times(x-6)~\textup{units}.](https://tex.z-dn.net/?f=6%5Ctimes%28x-6%29~%5Ctextup%7Bunits%7D.)
According to the question, we have
![6(x-6)=78\\\\\Rightarrow x-6=13\\\\\Rightarrow x=19.](https://tex.z-dn.net/?f=6%28x-6%29%3D78%5C%5C%5C%5C%5CRightarrow%20x-6%3D13%5C%5C%5C%5C%5CRightarrow%20x%3D19.)
Thus, the value of 'x' is 19 units.