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Math Help - Tiles around rectangle - Area or Perimeter?

  1. #1
    Junior Member Euclid Alexandria's Avatar
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    Question Tiles around rectangle - Area or Perimeter?

    From the book: "Area: A swimming pool is 20 feet wide and 40 feet long. If it is surrounded by square tiles, each of which is 1 foot by 1 foot, how many tiles are there surrounding the pool?"

    Although this question is posed in the chapter on area and volume, it appears in a section named "Applying the Concepts," which is not above questions that require concepts from previous chapters to be used for solving problems.

    If the tiles truly do surround the pool (or rectangle), then it seems like the problem is really asking for the perimeter. Also, I think this leaves a tile at each corner of the pool, to cover the outside corners.

    40 \cdot 2 + 20 \cdot 2 + 4 = 80 + 40 + 4 = 124\ tiles

    Or do you think the tiles should be considered as inside the corners of the pool?
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  2. #2
    Site Founder MathGuru's Avatar
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    I would say there should be a tile on the outside of each corner because the word surrounds is used.
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  3. #3
    Junior Member Euclid Alexandria's Avatar
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    Question Thanks (and happy 200th post)

    Just wanted to make sure I was thinking of it in the right way. Also, I now think I see why the question poses itself as a question of area. If it were a question of perimeter, I would only be measuring the lengths of straight lines. But I am measuring the area of the tiles.

    Another question about area asks, "A garden is rectangular with a width of 8 feet and a length of 12 feet. If it is surrounded by a walkway 2 feet wide, how many square feet of area does the walkway cover?"

    Again, I think this gives me four outside corners, this time measuring 2 X 2 each?

    A = 12 \cdot 4 + 8 \cdot 4 + 4 \cdot 4
    = 48 + 32 + 16
    = 96\ sq ft
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