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The rectangular garden represented in the figure above, with
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15 May 2018, 09:40
15 May 2018, 09:40
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#GREpracticequestion The rectangular garden represented in the figure above.jpg [ 10.29 KiB | Viewed 5320 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
Re: The rectangular garden represented in the figure above, with
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17 May 2018, 00:04
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
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
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04 Apr 2019, 17:33
04 Apr 2019, 17:33
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Expert Reply
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
