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Help for a mom

  1. Sep 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Here is the exact wording of my sons problem
    When a certain land owner died this l shaped plot of land was left to be shared among four children the only stipulation of the will was that the land must be divided into four congruent plots. show how this can be done. The figure given was one that looked like a square with a quarter of it removed. so that it resembled an L. As a mom, I'd say it resembled three toy blocks with 2 of them stacked next to the third
    2. Relevant equations

    none that I know of

    3. The attempt at a solution

    He tried mostly trial and error and I googled as much as I could. This is extra credit and he has given up, but it is driving me crazy. He is in 8th grade and is taking AP algebra/physics. I know this is probably a brainteaser or puzzle and should be a cinch for you all, but if you can help, I'd be most grateful

    Andy's Mom
  2. jcsd
  3. Sep 25, 2007 #2
    one strategy:
    Find total area (divide L into two rectangles, and are of rectangle is ab one side x another side)

    divide by 4

    try to isolate this 1/4 area into rectangles (which have area formula = ab)

  4. Sep 25, 2007 #3
    I had figured out, well actually I tried to explain to my son that the answer might have something to do with the area of the shape. I told him to make sure he drew his shape exactly four units by 4 units leaving out a 2by 2 unit piece. I figured working with those numbers would spare him dealing with fractions. All I got was this blank stare.

    I had figured out that each brother would get 3 square units but somehow I fixated on triangle shaped pieces and then kept trying to divide the land in half and then in half again.

    It suddenly dawned on me that the whole shape was essentially three units and that each parcel would be the same shape as the whole. It just took a little while to put the puzzle pieces together. It would have been easier it someone wouldn't have run off with my pencil.

    Thanks for sending me off in the right direction.
    I'll be able to sleep tonight with only songs from the school play running through my head.
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