A Persian rug set on a dining room floor measures a inches by b inches : Problem Solving (PS)

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A Persian rug set on a dining room floor measures a inches by b inches

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Math Expert

Joined: 02 Sep 2009

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A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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26 Nov 2014, 07:43

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Difficulty:

15% (low)

Question Stats:

80% (01:46) correct

20% (01:26) wrong

based on 72 sessions

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Tough and Tricky questions: Geometry.

A Persian rug set on a dining room floor measures a inches by b inches, which includes the actual rug design and a solid colored border c inches. Which algebraic expression below represents the area of the solid colored border in square inches?

A) ab − 4c
B) a + b − [(a − c) + (b − c)]
C) 2a + 2b − [2(a − 2c) + 2(b − 2c)]
D) ab − (a − c)(b − c)
E) ab − (a − 2c)(b − 2c)

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Spoiler: OA

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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26 Nov 2014, 08:26

See attached image.

Think of the length and widths of the carpet with the border as a and b. Then the length and width of the carpet without the border would be a - 2c and b - 2c. The formula for calculating the area of just the border would then be:

ab - (a-2c)(b-2c)

Answer is E.

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image.png [ 3.91 KiB | Viewed 1833 times ]

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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26 Nov 2014, 11:47

Total area including everything is just a*b
The area of the rug without the border is simply (a-2c)*(b-2c)--subtract 2c from each dimension as we have a uniform border on both sides, so we factor in a 2c

The area of just the border is the difference between the two values: ab-(a-2c)(b-2c)

Choice E

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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26 Nov 2014, 23:06

Answer = E) ab − (a − 2c)(b − 2c)

Refer diagram below:

Attachment:

rug.png [ 2.37 KiB | Viewed 1788 times ]

We require to find area of the shaded region

Total area = ab

Area of non-shaded region = (a-2c)(b-2c)

Area of shaded region = ab − (a − 2c)(b − 2c)
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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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27 Nov 2014, 07:34

Bunuel wrote:

Tough and Tricky questions: Geometry.

You all got it right. The answer is E.
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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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21 Oct 2017, 11:31

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