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Math Help - Shortest distance question

  1. #1
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    Question Shortest distance question

    I can't figure out what formula to use to solve this

    A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's 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 foot)?
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  2. #2
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    Quote Originally Posted by chickenwing View Post
    I can't figure out what formula to use to solve this

    A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's 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 foot)?
    Without using Calculus I can't prove its the shortest path, but what you need to do is walk a straight line from the SW corner of the lot to the SE corner of the building, then to the NE corner of the lot. Alternately you could go from the SW corner of the lot to the NW corner of the building, then to the NE corner of the lot.

    Since all the paths are straight lines you can use the Pythagorean Theorem to figure out each distance.

    -Dan
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    Quote Originally Posted by topsquark View Post
    Without using Calculus I can't prove its the shortest path, but what you need to do is walk a straight line from the SW corner of the lot to the SE corner of the building, then to the NE corner of the lot. Alternately you could go from the SW corner of the lot to the NW corner of the building, then to the NE corner of the lot.

    Since all the paths are straight lines you can use the Pythagorean Theorem to figure out each distance.

    -Dan
    I think I do not understand what you are saying or what the problem is saying.
    The shortest distance is,
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    I think I do not understand what you are saying or what the problem is saying.
    The shortest distance is,
    This is a good point. I had assumed the target was the NE corner of the lot.

    However, there is a shorter path on your diagram as well. SW corner of the lot to the NW corner of the building. Then to the NE corner of the building.

    -Dan
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    Quote Originally Posted by topsquark View Post
    This is a good point. I had assumed the target was the NE corner of the lot.

    However, there is a shorter path on your diagram as well. SW corner of the lot to the NW corner of the building. Then to the NE corner of the building.

    -Dan
    Since the terms "SW corner" and "NE corner" are not qualified in any way
    they should be assumed to be of the same entity; either the lot or the
    building.

    So the natural interpretation is Topsquarks, or the much less plausible distance
    from one corner of the building to the opposite one taking a path around
    the outside of the building (that is 200 ft)

    RonL
    Last edited by CaptainBlack; October 5th 2006 at 12:38 PM.
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  6. #6
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    Question

    Quote Originally Posted by ThePerfectHacker View Post
    I think I do not understand what you are saying or what the problem is saying.
    The shortest distance is,
    I think they want from the SW corner of the big lot to the the NE corner of the big lot; since they don't want you to cut acroos diagonally from corner to corner, I think the shortest way would be this: (I attached a file with a diagram) but how do I find the measurements?
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  7. #7
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    Quote Originally Posted by chickenwing View Post
    I can't figure out what formula to use to solve this

    A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's 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 foot)?
    Hi,

    I've attached a diagram to show which distances I've calculated.

    The total distance is: d = 2*sqrt(200² + 300²) ≈ 721 feet

    tschüss

    EB
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