If p is the perimeter of rectangle Q, what is the value of : DS Archive
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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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08 Jul 2008, 22:17
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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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much
Director
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08 Jul 2008, 23:01
fwl200 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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

answer to your question : yes each diagonal will bisect each other in a rectangle, but that doesn not mean that its a square. For it to be square, diagonals should bisect each other and andgle between them should be 90.

Now lest solve the question

if x and y are the two sides. we have to find out 2(x+y)

statement 1 : $$[m]x^2 + y^2 = 100$$[/m] . there coudl be more than one possible solution for (x,y) not suff
statement 2 : xy = 48, again not suff

combine : we know (x+y)^2 = x^2 + y^2 +2xy
mean we can find out x+y... Suff

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08 Jul 2008, 23:03
fwl200 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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.
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09 Jul 2008, 04:44
fwl200 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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

1. Rectangular has two diagonals which have the same length ==> the rectangular must be square.
So the perimeter = 4*(10/2)*aqrt(2)

2. area = 48, hmm we can not determine the length and width of rectangular.

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09 Jul 2008, 05:05
as said, the figure can be square too,
When combining 1 and 2 we can get the values by solving quadratic equations.
We get either 6 or 8.
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09 Jul 2008, 08:10
alpha_plus_gamma wrote:

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.

The square of length 10/sqrt(2) would not have an area of 48 - would be 50.

Quote:
combine : we know (x+y)^2 = x^2 + y^2 +2xy

I can't get how you arrive to this equation combining the two statements, can you expand on this?
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09 Jul 2008, 08:15
alpha_plus_gamma wrote:

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.

The square of length 10/sqrt(2) would not have an area of 48 - would be 50.

Quote:
combine : we know (x+y)^2 = x^2 + y^2 +2xy

I can't get how you arrive to this equation combining the two statements, can you expand on this?

we dint arrive at this equation by combining, We already know its a formula.

we need to find out (x+y). from combining the two statements we know x^2+y^2 from (1) and xy from (2) soe we can find out (x+y) using above formula.
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09 Jul 2008, 08:21
You're right - I just got confused by the "^" which we have to use in place of standard math notation!

Thanks
Director
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09 Jul 2008, 08:23
You're right - I just got confused by the "^" which we have to use in place of standard math notation!

Thanks

I should have used maths formula function provided on this site
$$(x+y)^2 = x^2 + y^2 +2xy$$
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09 Jul 2008, 08:34
lexis wrote:
fwl200 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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

1. Rectangular has two diagonals which have the same length ==> the rectangular must be square.
So the perimeter = 4*(10/2)*aqrt(2)

2. area = 48, hmm we can not determine the length and width of rectangular.

Who say this -> Rectangular has two diagonals which have the same length ==> the rectangular must be square. ?
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09 Jul 2008, 09:49
This comes from the 11th edition GMAT review book. The answer is C
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09 Jul 2008, 17:16
alpha_plus_gamma wrote:

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.

The square of length 10/sqrt(2) would not have an area of 48 - would be 50.

We are intersted in perimeter, not in area.

Above I was trying to say that since there are (atleast) 2 possibilities that the the rectangle can be a 8x6 rectangle or a square with side 10/sqrt(2), the perimeters will be different and thus 1) alone won't be suffcient.
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09 Jul 2008, 23:03
fwl200 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

----
Here's my question.
Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

p=2(a+b) ; a+b =?

1.sqrt(a^2+b^2) = 10
NS
2.ab= 48
NS
from 1 and 2 we can solve for a and b

C
Re: DS: Geometry   [#permalink] 09 Jul 2008, 23:03
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