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

10-72.

The picture at the right 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? Homework Help ✎

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