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The rectangular garden represented in the figure above, with dimension

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Bunuel
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The rectangular garden represented in the figure above, with dimension [#permalink] New post  26 Sep 2017, 23:24
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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

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pushpitkc
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The rectangular garden represented in the figure above, with dimension [#permalink] New post  26 Sep 2017, 23:40


The outer rectangle has dimensions x+4 and y+4,
when the dimensions of the inner rectangle have been given to be x and y.

The area of the walkway, will be the difference of the area of the outer rectangle and the area of the inner rectangle.

Mathematically, this can be represented as follows,
\((x+4)(y+4) - xy = xy + 4x + 4y + 16 - xy = 4x + 4y + 16\)

Therefore, 4x+4y+16(Option D) is the area of the walkway
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Re: The rectangular garden represented in the figure above, with dimension [#permalink] New post  03 Apr 2019, 07:17
inner rectangle has one side as x and the other side as y.
area is xy.

Outer rectangle has x+2+2= (x+4) as one side and (y+4) as another side.

area of the walk way = area of outer rectangle-area of the inner rectangle
i.e. (x+4)(y+4)-xy
xy+4x+4y+16-xy
4x+4y+16

D is the answer
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Re: The rectangular garden represented in the figure above, with dimension [#permalink] New post  04 Apr 2019, 18:33
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Bunuel wrote:

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

Show Spoiler
Attachment:
2017-09-27_1015_002.png


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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Mahi2409
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The rectangular garden with dimensions x feet by y feet, is surrounded [#permalink] New post  Updated on: 31 Jul 2019, 05:03
Bunuel wrote:
The rectangular garden 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


area of the walkway= area of larger rectangle - area of the inner rectangle
= (x+4) (y+4) - xy

Originally posted by Mahi2409 on 31 Jul 2019, 04:34.
Last edited by Mahi2409 on 31 Jul 2019, 05:03, edited 2 times in total.
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Re: The rectangular garden with dimensions x feet by y feet, is surrounded [#permalink] New post  31 Jul 2019, 04:56
Bunuel wrote:
The rectangular garden 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


new length ; (x+4) and width ( y+4)
original x &y
so area of walk way ; ( x+4)*(y+4) -xy
4x + 4y + 16
IMO D
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Re: The rectangular garden with dimensions x feet by y feet, is surrounded [#permalink] New post  31 Jul 2019, 05:10
Bunuel wrote:
The rectangular garden 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


Given: The rectangular garden with dimensions x feet by y feet, is surrounded by a walkway 2 feet wide.

Asked: Which of the following represents the area of the walkway, in square feet?

Area of walkway = (x+4)(y+4) - xy
= 4x+4y+16

IOM D
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Re: The rectangular garden with dimensions x feet by y feet, is surrounded [#permalink] New post  31 Jul 2019, 10:43
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This is a simple question on Mensuration. You just have to draw the figure right and the answer’s gonna be right in front of you to pick.

So, let us draw a figure to represent the situation described in the question.

Attachment:
31st July 2019 - Reply 3.JPG
31st July 2019 - Reply 3.JPG [ 22.55 KiB | Viewed 3344 times ]


From the diagram,

Area of the garden (the inner rectangle) = (x*y) square feet.

Area of the outer rectangle = [(x+4) * (y+4)] square feet.

So, area of the walkway = Area of the outer rectangle – Area of the inner rectangle

= (x*y) + 4x + 4y + 16 – (x*y)

= 4x + 4y + 16.

The correct answer option is D.

Hope this helps!
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Re: The rectangular garden with dimensions x feet by y feet, is surrounded [#permalink] New post  05 Aug 2019, 17:21
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Bunuel wrote:
The rectangular garden 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 area of the garden is xy square feet, and the area of the garden plus the walkway is (x + 4)(y + 4) square feet. Therefore, the area of the walkway, in square feet, is:

(x + 4)(y + 4) - xy = xy + 4y + 4x + 16 - xy = 4x + 4x + 16

Answer: D
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Re: The rectangular garden represented in the figure above, with dimension [#permalink] New post  12 Mar 2023, 14:28
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