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

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

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13 Nov 2005, 10:41
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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
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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...
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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)
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Re: DS - Perimeter of rectangle (OG11th, D48) [#permalink]

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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.

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

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

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

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

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30 Apr 2014, 02:29
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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.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html
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Re: If p is the perimeter of rectangle Q, what is the value of   [#permalink] 30 Apr 2014, 02:29
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