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The figure above shows a rectangular parcel of undeveloped land partit

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The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post Updated on: 02 Nov 2018, 03:58
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The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?


A. \((x^2) - x\)

B. \((x^2) + 9x\)

C. \(20x - (x^2)\)

D. \(9\)

E. \(20\)

Attachment:
AreaGeometry.PNG
AreaGeometry.PNG [ 3.47 KiB | Viewed 825 times ]

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Originally posted by pushpitkc on 02 Nov 2018, 03:55.
Last edited by Bunuel on 02 Nov 2018, 03:58, edited 1 time in total.
Edited the question.
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Re: The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post 02 Nov 2018, 07:41
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Area of Q = \(x^2\) ; Side = x
Area of R = 5x = x * length ; length of R = 5
Area of P = 4x = x * width ; width of P = 4

Area of the entire plot =\((x+4) * (x+5) = x^2 + 9x + 20\)

Area of S = \(x^2 + 9x + 20 - x^2 - 5x - 4x = 20\)
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Re: The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post 02 Nov 2018, 13:54
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Just adding on an alternate method to what pandeyashwin did...if the algebra intimidates you, keep in mind that one helpful technique on any geometry problem its o just draw the shape and label it. If you do that:

1) Notice that the upper left panel (Q) is a square with area x^2, so each side of it is x.

2) Then since R has an area of 5x and you know that its vertical height is the same as the height of Q, so its height is x, then its other dimension is 5.

3) Same logic for P. You know its horizontal width is the same as Q so also x, so its horizontal width must be 4 in order for its area to be 4x.

That leaves you with this diagram in the end:

Attachment:
SubdividedRectangle.png
SubdividedRectangle.png [ 13.53 KiB | Viewed 670 times ]


Note then that you know the dimensions of S: it has a height of 4 and a width of 5, so its area is 4 * 5 = 20.
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The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post 23 Jan 2019, 22:50
pushpitkc wrote:
Image
The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?


A. \((x^2) - x\)

B. \((x^2) + 9x\)

C. \(20x - (x^2)\)

D. \(9\)

E. \(20\)


Attachment:
AreaGeometry.PNG


Dear Moderator,
There may be a small typo here , the word " Parcel" may ought to have meant " Plot " perhaps. The word " parcel " seems unsuited in this context.Hope you will look into this. Thank you.
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Re: The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post 23 Jan 2019, 23:17
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stne wrote:
pushpitkc wrote:
Image
The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?


A. \((x^2) - x\)

B. \((x^2) + 9x\)

C. \(20x - (x^2)\)

D. \(9\)

E. \(20\)


Attachment:
The attachment AreaGeometry.PNG is no longer available


Dear Moderator,
There may be a small typo here , the word " Parcel" may ought to have meant " Plot " perhaps. The word " parcel " seems unsuited in this context.Hope you will look into this. Thank you.


All is correct there:
Attachment:
PS Geometry Land.JPG
PS Geometry Land.JPG [ 22.79 KiB | Viewed 415 times ]

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Re: The figure above shows a rectangular parcel of undeveloped land partit  [#permalink]

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New post 23 Jan 2019, 23:36
pushpitkc wrote:
Image
The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?


A. \((x^2) - x\)

B. \((x^2) + 9x\)

C. \(20x - (x^2)\)

D. \(9\)

E. \(20\)



Just follow what is given in the question and plot it as per the attached

Will give 4*5 = 20
Attachments

AreaGeometry.PNG
AreaGeometry.PNG [ 3.05 KiB | Viewed 399 times ]


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Re: The figure above shows a rectangular parcel of undeveloped land partit   [#permalink] 23 Jan 2019, 23:36
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