CPM Homework Banner

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 meters. The interior lines show roads connecting the houses. For what value of , , will the total length of the interior roads be the smallest?

Added to the rectangle, vertical segment from left endpoint of horizontal segment, perpendicular to top side, labeled 50, creating right triangle with horizontal leg labeled 100 minus x all divided by 2.

Total road length:

Rectangle, house at each vertex, 5 segments, 4 from each vertex to the fifth horizontal segment, in the center, labeled x, so that top & bottom left diagonal segments meet at the left endpoint of horizontal segment, & top & bottom right diagonal segments, meet at the right endpoint of horizontal segment