The calculation might have been incomplete, but it must have been done wrong, too. You get the number 164 if you ignore pi and take the square root of the area. Taking the square root of the area means taking the square root of pi, though, and pi is not squared in the formula for area of a circle.

First you divide the area, 27000, by pi, giving you 8261; then you take the square root of that and get 92.8. That's a maximum length of 93 feet of wire from the center of a circle to any place on the circumference, going in a straight line. Which won't happen.

So how much help is that? Quite enough for a round or square house. If the area were a square, it would be 164 feet on a side, or 82 feet from the center to the closest edge. To a corner it would be that times the square root of two, which is 116 feet, only 13% more than the similar number for a circle.

This gives a reasonable ballpark idea that you can count on distances being more than a hundred feet. How much more? It depends on how much the house differs from a square. If its "aspect ratio" is 2:1, 27,000 feet would be 116 x 232, so center to corner would be 129 feet.

Allowing for the fact that the house WON'T be a circle or square, but could easily be a 2:1 rectangle and not allowing for a tweaky shape, it seems reasonable to plan for at least 150 foot runs.

Did I mess up the arithmetic? Please check. And thanks. That was fun.