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# The figure above shows a large square formed by fitting three L shaped

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Math Expert
Joined: 02 Sep 2009
Posts: 51262
The figure above shows a large square formed by fitting three L shaped  [#permalink]

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11 Oct 2017, 00:00
1
5
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:41) correct 33% (02:05) wrong based on 57 sessions

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The figure above shows a large square formed by fitting three L shaped tiles and one small square tile together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

(A) 810
(B) 405
(C) 270
(D) 135
(E) 45

Attachment:

2017-10-11_1156_002.png [ 4.95 KiB | Viewed 1221 times ]

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Re: The figure above shows a large square formed by fitting three L shaped  [#permalink]

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11 Oct 2017, 00:40
ft=12 inch ==> inch =1/12 ft
Area of rectangular floor = 10 * 12 ft= 120 ft
Area of square = 8 inch * 8 inch = 8/12 ft * 8/12 ft=64/144 ft
Number of L tipes = Area of rect. floor / Area of square = (120ft * 144ft / 64 ft) * 3 = 810 L tipes

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Re: The figure above shows a large square formed by fitting three L shaped  [#permalink]

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11 Oct 2017, 19:27
1
Bunuel wrote:

The figure above shows a large square formed by fitting three L shaped tiles and one small square tile together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

(A) 810
(B) 405
(C) 270
(D) 135
(E) 45

Attachment:
2017-10-11_1156_002.png

1 ft = 12 inch (should be given in the question)

10 feet = 120 inch = 15* 8 inch
12 feet = 144 inch = 18* 8 inch

15 * 18 = 270 square tiles = 270*3 = 810 L-shaped
A
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Re: The figure above shows a large square formed by fitting three L shaped  [#permalink]

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11 Oct 2017, 21:40
1 feet = 12 inch
The area of the rectangle = (10*12)*(12*12) square inch
Area of the square = 8*8 square inch
Total number of the square required = (10*12)*(12*12) square inch/8*8 square inch
= 270
each have 3 L shaped object
So total objects = 270*3
810
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Re: The figure above shows a large square formed by fitting three L shaped  [#permalink]

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13 Oct 2017, 08:27
1
Bunuel wrote:

The figure above shows a large square formed by fitting three L shaped tiles and one small square tile together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

(A) 810
(B) 405
(C) 270
(D) 135
(E) 45

Attachment:
2017-10-11_1156_002.png

Let’s first determine the number of 8-in by 8-in large squares needed to cover the floor. To do so, let’s convert the dimensions of the floor to inches:

10 ft = 10 x 12 = 120 in and 12 ft = 12 x 12 = 144 in

Thus, the number of large squares needed is:

(120 x 144)/(8 x 8) = 15 x 18 = 270

We need 270 large squares; however, within each large square, there are 3 L-shaped tiles; thus, 270 x 3 = 810 L-shaped tiles are needed to cover the floor.

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Re: The figure above shows a large square formed by fitting three L shaped  [#permalink]

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15 Oct 2017, 05:49
Area of rectangular region in sq feet = 10 * 12 = 120
Since 1 feet = 12 inches
Area of rectangular region in sq inches = 120 * 144
Area of square in sq inches = 64
Number of squares required to cover rectangular region = (120 * 144) / 64 = 270
Number of L-shaped tiles in each square = 3
So, Total number of L-shaped tiles required = 270 * 3 = 810

Re: The figure above shows a large square formed by fitting three L shaped &nbs [#permalink] 15 Oct 2017, 05:49
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