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Math Help - Area problem using counting

  1. #1
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    Area problem using counting

    A picnic shelter in a park will cover a square region 30 ft. by 30 ft. (900 square ft.). The park has dimensions 60 ft. by 150 ft. If you want to build the picnic shelter using only a portion of the this space, 40 ft. by 130 ft., how many different locations in the park are possible for the placement of the picnic shelter?

    There is an accompanying small sketch with the problem: 1 rectangle that is 60 x 150 and the bordering edge along each side of the rectangle is shaded (the area the you cannot build the shelter in) and the 2nd rectangle (unshaded) within the the first rectangle.

    I'm not sure how to obtain the answer which is 22.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Re: Area problem using counting

    Personally, I don't like the wording of your question, but I can see what it is using.

    Have you made a picture for your work?

    Within the 40 ft by 130 ft that you can put the shelter, along the 40 ft, you can put the shelter in two ways:



    One of the left (pink) and one on the right (bluish).

    Now, how can you move the shelter in the unshaded area? Try moving the shelter down and count them. (move by 1 ft each time)

    Can you get the 22?
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  3. #3
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    Re: Area problem using counting

    I'm still confused as to how to get the 22 different ways; also, I made a small typo above: the shaded area may not have any part of the shelter in it so we are left with the unshaded (white) part.
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Re: Area problem using counting

    It's okay, I got it right and I got 22. The drawing I put up gives you 2 possible ways to place the shelter. Now, move the pink square down 1 ft to get a third, move it 2 ft down to get a forth and so on. You'll get two each time, one right and the other left, and along the 'height' if I may say so, you'll get exactly 11 possible ways on each side (ie 11 on the right and 11 on the left) giving a total of 22.

    Does that make it clearer?
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