How do you determine the smallest possible perimeter in a whole number not expression after factoring area?

Question

The area of a square garden, in square meters, is represented by the expression 169 - 182x + 49x² What is the smallest possible perimeter of the garder if x is a positive integer?

I factored 169 - 182x + 49x² to be (7x-13)² so the perimeter would be be 28x-52. But the answer to the perimeter is 24m with no variable.

How does the process to this answer work?

Answer 1

See that since $x$ is positive then the minimal value for the perimeter (an increasing function) is obtained by taking $x=0$.