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System of Linear Equations to Resolve Room Dimensions

  1. Aug 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Twelve equal rectangular ceiling panels are placed in a four long by three wide grid. Each panel is 150mm longer than it is wide. Between the panels runs an edge/middle strip which totals 40.0m in total length. (This runs round the whole perimeter and between each panel). By developing a system of linear equations what are the dimensions of the room?

    So I have been staring at this all day. I know I am missing something simple but translating the given detail into something I can develop and solve is just a block at the moment. I would love some guidance if possible.


    2. Relevant equations

    ??

    3. The attempt at a solution

    Have made many but none are correct!
     
  2. jcsd
  3. Aug 6, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The phrase "The attempt at a solution" does NOT refer only to successfu ones. If you have made many attempts, you should be able to show one[b\]. Seeing your mistakes will help us know what hints will help you.
     
  4. Aug 6, 2013 #3
    Ok well the best I have come up with so far is 4(4w+0.6)+5(3w)=40

    Where w = width
     
  5. Aug 6, 2013 #4
    Actually I think I have it now.

    where w = width and l = length.

    1. w=l-0.15
    2. 16l+15w=40

    Substituting into Eq 2

    16l+15(l-0.15)=40
    16l+15l-2.25=40
    l=1.36m

    Therefore:

    w=1.36-0.15=1.21m

    So overall room dimensions are 3w=3.63m and 4l=5.44m

    That seems to work out and follow fairly sensible logic I think.
     
  6. Aug 7, 2013 #5

    verty

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    Homework Helper

    So the strip runs between the tiles? I think you must calculate half the sum of the length of any side that touches another tile. Set this to 40 and you'll be able to find the solution.
     
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