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If MN = 10, what is the perimeter of the rectangle?

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Math Expert
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Joined: 02 Sep 2009
Posts: 56271
If MN = 10, what is the perimeter of the rectangle?  [#permalink]

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New post 17 Sep 2018, 21:50
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (02:02) correct 50% (02:18) wrong based on 55 sessions

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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If MN = 10, what is the perimeter of the rectangle?  [#permalink]

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New post 17 Sep 2018, 23:30
2
Bunuel wrote:
Image
If MN = 10, what is the perimeter of the rectangle?

(1) The area of the rectangle is 50
(2) NO = LM = 6


Attachment:
The attachment image010.jpg is no longer available


Individually statements rae not suficient to find out the perimter of the given rectangle.

Combined, Please refer the affixed diagram,
Perimeter= 12+x+12+x+y+y=24+2(x+y)
We need to find out the value of x+y.
From the diagram,
a)\(x^2+y^2=10^2\)
b) (12+x)*y=50
We have two equations and two variables.Hence, the value of x and y can be determined.(only positive values are acceptable)
Excact computation is not required.
Sufficient to determine (x+y), hence the perimeter.
Ans. (C)
Attachments

Rectangle perimeter.jpg
Rectangle perimeter.jpg [ 24.07 KiB | Viewed 386 times ]


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Re: If MN = 10, what is the perimeter of the rectangle?  [#permalink]

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New post 25 Sep 2018, 21:53
PKN wrote:
Bunuel wrote:
Image
If MN = 10, what is the perimeter of the rectangle?

(1) The area of the rectangle is 50
(2) NO = LM = 6


Attachment:
image010.jpg


Individually statements rae not suficient to find out the perimter of the given rectangle.

Combined, Please refer the affixed diagram,
Perimeter= 12+x+12+x+y+y=24+2(x+y)
We need to find out the value of x+y.
From the diagram,
a)\(x^2+y^2=10^2\)
b) (12+x)*y=50
We have two equations and two variables.Hence, the value of x and y can be determined.(only positive values are acceptable)
Excact computation is not required.
Sufficient to determine (x+y), hence the perimeter.
Ans. (C)



Exact computation is not required even though the degree of freedom is two, we can only accept the positive real values. What if we get irrationals or non terminating decimals ? I always end up computing in DS questions. Is there a way we can generalize ?
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Re: If MN = 10, what is the perimeter of the rectangle?   [#permalink] 25 Sep 2018, 21:53
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