A homeowner is about to construct a large patio in her backyard. She designed the geometrical pattern above and plans to use white and gray paving stones to construct the patio in that pattern. The gray paving stones she needs are squares; gray squares are available for purchase in virtually any size. White paving stones are not available for purchase in the shape she needs. Therefore, the homeowner will purchase regular hexagonal white stones and have them cut to her specifications, as indicated by the dashed-line detail on the right side of the figure. The hexagonal white stones the homeowner can purchase are 6 feet in perimeter. What is the perimeter, in feet, of the gray square stones the homeowner should purchase?
Comments (2)
Please explain how 1/(2^1/2)=(2^1/2)/2? this is a big leap that was unexplained
Sorry about that. Conventionally, we don’t leave radicals in denominators, so when we have
, we multiply it by a useful form of 1, 
.