SOLUTION: A city block 500 feet by 500 feet has a large building 300 feet by 300 feet in the exact center. The rest of the block is an unobstructed paved lot. What is the shortest distance f

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Question 182694: A city block 500 feet by 500 feet has a large building 300 feet by 300 feet in the exact center. The rest of the block is an unobstructed paved lot. What is the shortest distance from the SW corner to the NE corner of the city block, going through the paved lot (to the nearest foot)??
Not sure on what I need to do here...
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
well,if the building wasnt there we know we could go straight across the diagaonal from the sw corner to the ne corner. We can still travel the diagonal until we come to the building and then we either have to travel along the west and north sides or the south and east sides of the building until we reach the ne corner of the building ......from there we travel the diagonal to the ne corner of the block.
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so we know that we have to travel along 2 sides of the building and two equal diagonals.
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the sides are easy to figure...2(300)=600 feet.......now we only need to figure out the distance of the diagonals(which again are equal),so figure out the distance of one and multiply by two.
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we can create 2 legs which are 200 feet each. One leg is from the sw corner of the building to the south side of the block and the other leg is from the vertex, we just created on the south side of the block to the sw corner. Using pathagorean's theorem we have the two legs and can find the hypothenuse with that information.
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the diagonal we are looking for is the hypothenuse and we will call it c
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so
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=282.84
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2 diagonals=2(282.84)=565.68
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so the shortest distance total would be 600+565.68=1165.68 feet