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

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

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17 Sep 2018, 21:50
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Difficulty:

65% (hard)

Question Stats:

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

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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 [ 4.32 KiB | Viewed 441 times ]

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

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17 Sep 2018, 23:30
2
Bunuel wrote:

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 [ 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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25 Sep 2018, 21:53
PKN wrote:
Bunuel wrote:

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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