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Math Help - geometry

  1. #1
    Junior Member
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    Jul 2008
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    geometry

    A rectangular room 4m by 3m and 2m high. A Snail is at A and wants to get to R. Find the shortest path it could crawl without crossing the ceiling. Find the length of this path and draw it on a 3D sketch of the room.

    Your group has decide, with great wisdom, that it's strategy is to imagine the room is a box with the edges cut so that it lays flat. On sketches of the fattened room, plot possible pathways and calculate the distances covered by the Snail along these pathways.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    The ant is not allowed to use rhe ceiling PQRS.

    a) Trial 1.
    Cut the box such so that you can lay/spread where a portion is like so:
    It's a horizontal rectangular diagram whose bottom side is ABQPA and whose top side is DCRSD. D is directly above A, C above B, R above Q, S above P, D above A.
    The ant would travel a straight line from A to R.
    By Pythagorean theorem,
    distance, d^2 = (AB +BQ)^2 +(QR)^2
    d = sqrt[(4 +2)^2 +(3)^2] = sqrt(45) = 6.708 meters --------**


    a) Trial 2.
    Cut the box such so that you can lay/spread where a portion is like so:
    It's a vertical rectangular diagram whose left side is ADSPA and whose right side is BCRQB. B is to the right of A, C of D, R of S, Q of P, B of A.
    The ant would travel a straight line from A to R.
    By Pythagorean theorem,
    distance, d^2 = (AB)^2 +(BC +CR)^2
    d = sqrt[(4)^2 +(3 +2)^2] = sqrt(41) = 6.403 meters --------**
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