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A rectangular rug with side lengths of 2 feet and 6 feet is placed on

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A rectangular rug with side lengths of 2 feet and 6 feet is placed on  [#permalink]

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New post 11 Feb 2020, 03:02
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A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square ‡floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the fl‡oor, what fraction of the area of the fl‡oor is not covered by the rug?

A. 3/16
B. 1/4
C. 1/2
D. 13/16
E. 7/8

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Re: A rectangular rug with side lengths of 2 feet and 6 feet is placed on  [#permalink]

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New post 11 Feb 2020, 03:15
- Area of rectangular rug: 6*2 = 12 sq feet
- Area of square floor: 64 sq feet

Area NOT covered by rug: 52/64 or 13/16

Option D
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Re: A rectangular rug with side lengths of 2 feet and 6 feet is placed on  [#permalink]

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New post 11 Feb 2020, 21:39
Bunuel wrote:
A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square ‡floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the fl‡oor, what fraction of the area of the fl‡oor is not covered by the rug?

A. 3/16
B. 1/4
C. 1/2
D. 13/16
E. 7/8


Solution


    • Area of the rectangular rug \(= 2*6 = 12\) sq. feet
    • total area of the floor = 64 sq. feet.
    • So, area of uncovered floor \(= 64 – 12 = 52\) sq. feet.
    • Hence, the fraction of the floor which is uncovered = area of uncovered floor/ total area of the floor \(= \frac{52}{64} = \frac{13}{16}\)
Thus, the correct answer is Option D.
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A rectangular rug with side lengths of 2 feet and 6 feet is placed on  [#permalink]

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New post 16 Feb 2020, 05:45
Bunuel wrote:
A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square ‡floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the fl‡oor, what fraction of the area of the fl‡oor is not covered by the rug?

A. 3/16
B. 1/4
C. 1/2
D. 13/16
E. 7/8


The area of the rug is 2 x 6 = 12 square feet. Therefore, the fraction of the floor covered by the rug is 12/64, and the area of the floor not covered by the rug is 1 - 12/64 = 52/64 = 13/16.

Answer: D
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A rectangular rug with side lengths of 2 feet and 6 feet is placed on   [#permalink] 16 Feb 2020, 05:45
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