### Home > CALC > Chapter 10 > Lesson 10.1.7 > Problem10-72

10-72.

The picture below shows a housing complex consisting of four houses. Each house sits at the corner of a square that measures $100$ meters on the side. The interior lines show roads connecting the houses. For what value of $x$, $0 ≤ x ≤ 100$, will the total length of the interior roads be the smallest?

$50+4\sqrt{50^2+\Big(\frac{100-x}{2}\Big)^2}$