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The rectangular pool represented in the figure above, with d
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10 Mar 2019, 06:46
10 Mar 2019, 06:46
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#GREpracticequestion The rectangular pool represented in the figure above.jpg [ 14.05 KiB | Viewed 1544 times ]
The rectangular pool 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. \(4x + 4y + 16\)
D. \(4x + 4y + 32\)
E. \(8x + 8y + 32\)
Re: The rectangular pool represented in the figure above, with d
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17 Mar 2019, 17:54
17 Mar 2019, 17:54
Expert Reply
This one's a bit funky. But to get from the walkway to the edge of the pool, we have to walk 2 feet. Then we have the whole width of the pool, x. Then, to talk from the pool to the edge of the walkway on the other side, we have to walk another 2 feet. The total width of the walkway, then, is 2 + x + 2 = 4 + x.
Following that same process, the length of the pool will be 2 + y + 2 = 4 + y.
The area is the length times the width, so (4 + x)*(4 + y).
To multiply those, we FOIL:
First terms: 4*4 = 16
Outside terms: 4*y = 4y
Inside terms: x*4 = 4x
Last terms: x*y = xy
Then we add them all up: 16 + 4x + 4y + xy
That's the entire area enclosed by the walkway. Of that area, though, the pool is taking up an area of xy. So we need to subtract that term, and we'll be left with just 16 + 4x + 4y as the area of the walkway itself.
Following that same process, the length of the pool will be 2 + y + 2 = 4 + y.
The area is the length times the width, so (4 + x)*(4 + y).
To multiply those, we FOIL:
First terms: 4*4 = 16
Outside terms: 4*y = 4y
Inside terms: x*4 = 4x
Last terms: x*y = xy
Then we add them all up: 16 + 4x + 4y + xy
That's the entire area enclosed by the walkway. Of that area, though, the pool is taking up an area of xy. So we need to subtract that term, and we'll be left with just 16 + 4x + 4y as the area of the walkway itself.
gmatclubot
Re: The rectangular pool represented in the figure above, with d [#permalink]
17 Mar 2019, 17:54
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