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# The rectangular rug shown in the figure above has a floral border 1

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Math Expert
Joined: 02 Sep 2009
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The rectangular rug shown in the figure above has a floral border 1 [#permalink]

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21 Sep 2017, 23:40
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The rectangular rug shown in the figure above has a floral border 1 foot wide on all sides. What is the area, in square feet, of that portion of the rug that excludes the border?

(A) 28
(B) 40
(C) 45
(D) 48
(E) 53

[Reveal] Spoiler:
Attachment:

2017-09-22_1138.png [ 2.74 KiB | Viewed 512 times ]
[Reveal] Spoiler: OA

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Re: The rectangular rug shown in the figure above has a floral border 1 [#permalink]

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22 Sep 2017, 18:34
Bunuel wrote:

The rectangular rug shown in the figure above has a floral border 1 foot wide on all sides. What is the area, in square feet, of that portion of the rug that excludes the border?

(A) 28
(B) 40
(C) 45
(D) 48
(E) 53

Attachment:

2017-09-22_1138ed.png [ 7.08 KiB | Viewed 370 times ]

Typically these border problems require quadratic equations. This one does not.

We need the area of "that portion of the rug that excludes the border." The part without the border is the smaller, inside rectangle.

The length of the larger rectangle is 9. The width of the border is 1 foot -- on both sides of the smaller, inside rectangle.
The width of the larger rectangle is 6. Again, the width of the border is 1 foot on both sides.

So the length of the smaller rectangle is 9 feet - 1 foot - 1 foot = 7 feet
The width of the smaller rectangle is 6 feet - 1 foot - 1 foot = 4 feet

The area, in square feet, of the portion of the rug that does not contain the border is
L * W = 7 * 4 = 28

ANSWER A
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Re: The rectangular rug shown in the figure above has a floral border 1 [#permalink]

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22 Sep 2017, 20:20

Since the rectangular rug contains of two foot of the floral border
on its end both on the length and the breadth, the area of the
rug(excluding the border) must be $$(9-2)(6-2) = 7*4 = 28$$

Therefore, the area of the rug(except the border) is 28 square feet(Option A)
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Re: The rectangular rug shown in the figure above has a floral border 1   [#permalink] 22 Sep 2017, 20:20
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# The rectangular rug shown in the figure above has a floral border 1

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