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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]
11 Mar 2013, 01:32

nave81 wrote:

In the diagram above, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles?

(1) ABCD is a square.

(2) EFGH is a square.

Figure attached Suppose the dimention of the tiles are l*b

STAT1 Let side of Square ABCD = a then if you consider side AB then AB = a = 3l + 2b

if you consider side AD then AD = a = 4l

so, 4l = 3l + 2b or, l =2b

Also, we know that a = 4l so, l = a/4 b = l/2 = a/8 So, we can find the area of the tile in terms of "a" Area of all the tiles = (constant)* a^2 So, we can find the percentage of area occupied by tile = ((constant)* a^2 / a^2 ) * 100 So, SUFFICIENT

STAT2 Let side of EFGH = c then if you consider EF then EF = c = 3l

if you consider EH then EH = c = 2l + l-b + l-b = 4l-2b

=> 3l = 4l-2b l = 2b

And we have c = 3l => l = c/3 b = l/2 = c/6

AB = 4l = 4c/3

So, we can find area of ABCD in terms of C And we can find area of the tiles in terms of c So, we can find the percentage of area occupied by tiles So, SUFFICIENT

Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]
03 Oct 2014, 06:30

(1) SUFFICIENT: Let the length (longer dimension) of each rectangular tile be called L, and the width (shorter dimension) of each tile W. Then each horizontal side of square ABCD has total length 2W + 3L, and each vertical side has total length 4L.

Because ABCD is a square, these total lengths must be equal: 2W + 3L = 4L, which reduces to L = 2W. Therefore, each side of square ABCD is equal to 4L = 8W, and the total area of square ABCD is (8W)(8W) = 64W2.

The total area of the tiles is 14(L × W) = 14(2W × W) = 28W2. The desired fraction is thus (28W2)/(64W2) = 28/64. There is no need to reduce this fraction; the statement is sufficient.

(2) SUFFICIENT: Let the length (longer dimension) of each rectangular tile be called L, and the width (shorter dimension) of each tile W. Then each horizontal side of square ABCD has total length 3L, and each vertical side has total length 4L – 2W.

Because EFGH is a square, these total lengths must be equal: 3L = 4L – 2W, which reduces to L = 2W. Therefore, each side of square ABCD is equal to 3L = 6W.

In turn, ABCD must also be a square, since each of its sides is 2W longer than the corresponding side of EFGH (i.e., longer by W on each side). Therefore, each side of ABCD is equal to 6W + 2W = 8W, and the total area of square ABCD is (8W)(8W) = 64W2.

The total area of the tiles is 14(L × W) = 14(2W × W) = 28W2. The desired fraction is thus (28W2)/(64W2) = 28/64. There is no need to reduce this fraction; the statement is sufficient.

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