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# Does the rectangle have an area less than 30? (1) Perimeter

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Does the rectangle have an area less than 30? (1) Perimeter [#permalink]  18 Aug 2009, 17:43
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Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10
Manager
Joined: 14 Aug 2009
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Re: Area of rectangle [#permalink]  19 Aug 2009, 06:08
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yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10

for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\sqrt{100-X^2}

when X^2=50 or X=\sqrt{50}, Smax=50>30

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Senior Manager
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Re: Area of rectangle [#permalink]  05 Jan 2010, 13:17
flyingbunny wrote:
yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10

for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\sqrt{100-X^2}

when X^2=50 or X=\sqrt{50}, Smax=50>30

Dont think this is correct....

ST1 - SUFF for sure....
ST2 - gives that area is more than 30... therefore is very much sufficient to answer the question....

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Senior Manager
Joined: 22 Dec 2009
Posts: 366
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Kudos [?]: 178 [0], given: 47

Re: Area of rectangle [#permalink]  05 Jan 2010, 13:20
jeeteshsingh wrote:
flyingbunny wrote:
yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10

for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\sqrt{100-X^2}

when X^2=50 or X=\sqrt{50}, Smax=50>30

Dont think this is correct....

ST1 - SUFF for sure....
ST2 - gives that area is more than 30... therefore is very much sufficient to answer the question....

Oops.... sorry its A.... My mistake... I failed to consider that diagonal is less than 10.. hence the area could be 50 or less.....
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Manager
Joined: 27 Aug 2009
Posts: 148
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Re: Area of rectangle [#permalink]  05 Jan 2010, 14:31
Manager
Joined: 24 Jul 2009
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Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
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Re: Area of rectangle [#permalink]  09 Jan 2010, 20:20
Can someone provide another example for why STMT 2 is insufficient?
I can see that the area's < 48 since the diagonal's < 10.
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Manager
Joined: 24 Jul 2009
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Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
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Kudos [?]: 21 [0], given: 10

Re: Area of rectangle [#permalink]  09 Jan 2010, 20:40
gottabwise wrote:
Can someone provide another example for why STMT 2 is insufficient?
I can see that the area's < 48 since the diagonal's < 10.

Rephrase of ? - Are l & w < 5 & 6?
(1) 2l+2w=20 l+w=10 max 5, 5; max area 25; 25<30 SUFF
(2) 1/2 rectangle=right triangle; a^2+b^2=c^2 c<10 (6-8-10 right triangle); sides less than 6 & 8
given that, does the possibility of the l & w being any combo of #'s < 6&8 make it INS?
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Re: Area of rectangle [#permalink]  09 Jan 2010, 22:47
Thanks for the g8 explanation
Re: Area of rectangle   [#permalink] 09 Jan 2010, 22:47
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# Does the rectangle have an area less than 30? (1) Perimeter

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