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

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Math Expert
Joined: 02 Sep 2009
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A rectangular rug with side lengths of 2 feet and 6 feet is placed on  [#permalink]

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11 Feb 2020, 03:02
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Difficulty:

25% (medium)

Question Stats:

84% (01:26) correct 16% (01:18) wrong based on 32 sessions

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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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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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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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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.

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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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