It is currently 18 Nov 2017, 13:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If p is the perimeter of rectangle Q, what is the value of

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Jul 2005
Posts: 48

Kudos [?]: 8 [1], given: 0

If p is the perimeter of rectangle Q, what is the value of [#permalink]

### Show Tags

13 Nov 2005, 10:41
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:48) correct 27% (00:47) wrong based on 210 sessions

### HideShow timer Statistics

If p is the perimeter of rectangle Q, what is the value of p?

(1) Each diagonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html
[Reveal] Spoiler: OA

Kudos [?]: 8 [1], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 322 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

13 Nov 2005, 10:51
I would say c

well A just tells us that rectangular is symetrical...but the sides could be any variable...say

x and y are the two sides then...x^2+Y^2=100....x^2 could be 50, or it could be 10...or 25...we dont know...

(2) just tells the area we dont know what the length are.

combining...well I think that should be sufficient...

Kudos [?]: 322 [0], given: 2

VP
Joined: 22 Aug 2005
Posts: 1111

Kudos [?]: 124 [0], given: 0

Location: CA

### Show Tags

13 Nov 2005, 11:05
let x,y be side

given: x^2 + y^2 = 100
xy = 48

we can get:
(x+y)^2 = 100 + 96 = 196
(x+y) = 14

(x-y)^2 = 100 - 96 = 4
(x-y) = 2

we can find x,y and then perimeter 2(x+y)
_________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

Kudos [?]: 124 [0], given: 0

VP
Joined: 06 Jun 2004
Posts: 1050

Kudos [?]: 185 [0], given: 0

Location: CA
Re: DS - Perimeter of rectangle (OG11th, D48) [#permalink]

### Show Tags

13 Nov 2005, 12:52
omomo wrote:
If p is the perimeter of rectangle Q, what is the value of p?
1) Each diagonal of rectangle Q has length 10.

2) The area of rectangle Q is 48

Just a question...if we know that it's a right triangle and the length of hypotenuse...can't we assume it's 6-8-10 right triangle right off the bat???

Hmmm, I think the definition of a rectangle states that "a four-sided figure with opposite sides of equal length and all its angles right angles". So a rectangle here could also mean a square. So we cannot assume its a 6-8-10 right triangle. The sides could be 10/sqrt2 as well.

So with that being said...(1) is insufficient.

(2) Let x and y be the sides of the rectangle. xy=48. Insufficient. As x and y could be sqrt 48.

(1) and (2) together, x^2 + y^2 = 10^2, and xy = 48

x and y are 6 or 8, since we are asked for 2(x+y), we could solve for the perimeter.

Kudos [?]: 185 [0], given: 0

Manager
Joined: 20 Oct 2013
Posts: 65

Kudos [?]: 3 [0], given: 27

Re: If p is the perimeter of rectangle Q, what is the value of [#permalink]

### Show Tags

29 Apr 2014, 11:50
as its a rectangle and we know that the diagonal is 10... cant we consider the rectangle to be 2 triangles of 45:45:90... and assume sides to be in ratio 1:1:root 2??? that ways 1st equation is sufficient.
_________________

Hope to clear it this time!!
GMAT 1: 540
Preparing again

Kudos [?]: 3 [0], given: 27

Director
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 865 [0], given: 724

Location: India
GPA: 3.21
Re: If p is the perimeter of rectangle Q, what is the value of [#permalink]

### Show Tags

29 Apr 2014, 22:20
nandinigaur wrote:
as its a rectangle and we know that the diagonal is 10... cant we consider the rectangle to be 2 triangles of 45:45:90... and assume sides to be in ratio 1:1:root 2??? that ways 1st equation is sufficient.

If you assume rectangle to be 2 triangles of 45:45:90, then it makes a square and the sides will be 10/$$\sqrt{2}$$ :10/$$\sqrt{2}$$: 10

Also it is not given that the sides are integers so we can have $$x^2+y^2=10^2$$. Now x=$$\sqrt{99}$$ and y= 1 then perimeter, p= 2($$\sqrt{99}$$ +1)

Now if x=6,y=8 then perimeter, p= 2*(14)= 28.

2 different answers are possible using St1 and therefore it is not alone

From St 2 we have xy=48 (Many combinations possible such as x=4,y=12, p=32 or x=6,y=8, p=28). Not sufficient

Combining we get, only 1 possible value of x=6and y=8 or vice versa meet both conditions.

Ans is C
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 865 [0], given: 724

Manager
Joined: 20 Oct 2013
Posts: 65

Kudos [?]: 3 [0], given: 27

Re: If p is the perimeter of rectangle Q, what is the value of [#permalink]

### Show Tags

30 Apr 2014, 02:00
Thanks wounded tiger. I also wanted to know if i can find a summary of integer rules. I am weak at number properties.
_________________

Hope to clear it this time!!
GMAT 1: 540
Preparing again

Kudos [?]: 3 [0], given: 27

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132606 [0], given: 12326

Re: If p is the perimeter of rectangle Q, what is the value of [#permalink]

### Show Tags

30 Apr 2014, 02:29
Expert's post
4
This post was
BOOKMARKED
If p is the perimeter of rectangle Q, what is the value of p?

Question: $$P=2(a+b)=?$$

(1) Each diagonal of rectangle Q has length 10. $$d^2=a^2+b^2=100$$. Not sufficient.
(2) The area of rectangle Q is 48. $$ab=48$$. Not sufficient.

(1)+(2) Square P --> $$P^2=4(a^2+b^2+2ab)$$. Now as from (1) $$a^2+b^2=100$$ and from (2) $$ab=48$$, then $$P^2=4(a^2+b^2+2ab)=4(100+2*48)=4*196$$ --> $$P=\sqrt{4*196}=2*14=28$$. Sufficient.

Similar questions to practice:
if-the-diagonal-of-rectangle-z-is-d-and-the-perimeter-of-104205.html
what-is-the-area-of-rectangular-region-r-105414.html
what-is-the-perimeter-of-rectangle-r-96381.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html
_________________

Kudos [?]: 132606 [0], given: 12326

Re: If p is the perimeter of rectangle Q, what is the value of   [#permalink] 30 Apr 2014, 02:29
Display posts from previous: Sort by