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The rectangular garden represented in the figure above, with

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The rectangular garden represented in the figure above, with [#permalink] New post 15 May 2018, 09:40
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#GREpracticequestion The rectangular garden represented in the figure above.jpg
#GREpracticequestion The rectangular garden represented in the figure above.jpg [ 10.29 KiB | Viewed 1928 times ]


The rectangular garden represented in the figure above, with dimensions x feet by y feet, is surrounded by a walkway 2 feet wide. Which of the following represents the area of the walkway, in square feet?

(A) 2x + 2y + 4

(B) 2x + 2y + 16

(C) 4x + 4y + 8

(D) 4x + 4y + 16

(E) 4x + 4y + 32
[Reveal] Spoiler: OA

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Re: The rectangular garden represented in the figure above, with [#permalink] New post 17 May 2018, 00:04
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The area of the garden = \(x * y = xy\)
The area of the garden + walkway = \((x+4)(y+4)\); since the width of the walkway is 2 feet wide hence 2+2 = 4 feet will be added to length and width of the garden for a combined length and breadth as the garden is surrounded by walkway

the area of walkway = \((x+4)(y=4) - xy\)
simplifying the area of the garden + walkway = \(xy + 4x + 4y + 16\)
therefore, area of the walkway = \(xy + 4x + 4y + 16 - xy = 4x + 4y + 16\)
option D
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Re: The rectangular garden represented in the figure above, with [#permalink] New post 04 Apr 2019, 17:33
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Carcass wrote:
Attachment:
#GREpracticequestion The rectangular garden represented in the figure above.jpg


The rectangular garden represented in the figure above, with dimensions x feet by y feet, is surrounded by a walkway 2 feet wide. Which of the following represents the area of the walkway, in square feet?

(A) 2x + 2y + 4

(B) 2x + 2y + 16

(C) 4x + 4y + 8

(D) 4x + 4y + 16

(E) 4x + 4y + 32



The garden (interior rectangle) is x feet wide so the larger rectangle is (x + 4) feet wide. Similarly, the garden’s length is y feet, so the exterior rectangle’s length is (y + 4) feet long. Thus, the area of the larger rectangle is (x + 4)(y + 4). The area of the garden itself is xy. We can thus create the expression for the area of the walkway as the difference of the two areas::

(x + 4)(y + 4) - xy

xy + 4x + 4y + 16 - xy

4x + 4y + 16

Answer: D
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Re: The rectangular garden represented in the figure above, with   [#permalink] 04 Apr 2019, 17:33
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