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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
Trying to figure out what I did wrong here. I got B .

A: length of one tile = perim / 4 = 9. tiles to cover width side =72/9 = 8 tiles to cover length side = 108/9 = 12. Whole area = 8*12 = 96
B: length of one tile = sqrt(area) = 3. tiles to cover width side =72/3 = 24 tiles to cover length side= 36. two sides each for rectangular border = 24*2 + 36*2 = 120
-- we already know B is greater, but to actually cover the whole border, we would need to cover the four corners with tiles too, bringing the total of B to 124.

did i misunderstand part of the question? Thanks
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
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OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
1
Carcass wrote:
OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.


Thanks for posting this, but does this mean the answer should be B (the Show Answer link above shows A)? Thx
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
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pster79 wrote:
Carcass wrote:
OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.


Thanks for posting this, but does this mean the answer should be B (the Show Answer link above shows A)? Thx


:(

The answer is indeed B but the book reports A in the OA. The explanation B
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
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