What's the shortest distance ?

Question

A city block 500 feet by 500 feet is an unobstructed paved lot, except for small office building 100 feet by 100 feet, centered in the middle of the block. What is the shortest distance from the SW corner to the NE corner, going through the paved lot and along (but not through) the building ( to the nearest too)? Please show work.

Answer 1

oops, sorry!  Both of the other answers assume that the shortest total length is from one corner to the nearest corner of the building, around 1/2 of the building, then finish by going straight to the other corner....a total by my figures of about  765 feet.

A shorter route would be from one corner to the corner of the building OPPOSITE the nearest corner, i.e., just missing the building, then straight to the opposite corner...a total of 721 feet.

My path takes me , for ex, from the NW corner of the lot to the NE corner of the building, to the SE corner of the lot.

Answer 2

500(square)+500(square)=sq root of 500,000=700

700 feet diagonally across the room.

100(sq)+100(sq)=sq root of 20,000=140(diagonal distance of the middle office)

700-140=560+100(south side of office)+100(east side of office)=760 feet.  The shortest distance SW to NE diagonally across the room.

Answer 3

you can solve this easily by drawing a diagram.

teh result, assuming you go in straight lines, is teh diagonal of teh block, minus teh diagonal of teh building, plus two times teh length of teh side of teh building.

draw a diagram and you will see why.