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Area of Goalbox vs. Area of Penalty Box (rationals)

  1. Feb 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Area of goal box (soccer field) is described with (10x^2) / 27 and area of penalty box is described with (22x^2) / 9 . Determine how many times greater in size the penalty box is compared to the goal box.

    2. Relevant equations



    3. The attempt at a solution

    I created the areas of the boxes based from dimensions, and simplified to what I have given (assume they are correct). Just don't get how to figure out that size difference (which is terrible since I just completed this question on the Fermat math contest for Waterloo earlier today, no problem, but I get thrown off in even easier math?)
     
  2. jcsd
  3. Feb 19, 2008 #2
    read the question again. you don't even have to know the areas... it is simply asking for a ratio between the two
     
  4. Feb 19, 2008 #3
    well ya... Simple ratio is (10x^2)/27 : (22x^2)/9 ... sooo.. would I then put that into fraction form (not sure which on top vs bottom for this situation), then simplify as far as possible...?
     
  5. Feb 20, 2008 #4

    HallsofIvy

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    "Determine how many times greater in size the penalty box is compared to the goal box."
    You want "penalty box" over "goal box".

    (22x^2) / 9 over (10x^2) / 27 which is the same as (22x^2)/9 times 27/(10x^2).
     
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