### Home > APCALC > Chapter 10 > Lesson 10.1.7 > Problem10-89

10-89.

The picture at the right shows a housing complex consisting of four houses. Each house sits at the corner of a square with sides that measure $100$ meters. 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?

Total road length:

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