## Do you know a Rectangle when you see one?

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### Do you know a Rectangle when you see one?

by dtweah » Tue May 12, 2009 5:47 am
Among all rectangles of area 3, what is the smallest possible value of the sum of the lengths of
its diagonals?

a. &#8730;8
b. 2&#8730;6
c. 2&#8730;10
d. 8
e. 10

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### Re: Do you know a Rectangle when you see one?

by marcusking » Tue May 12, 2009 6:38 am
dtweah wrote:Among all rectangles of area 3, what is the smallest possible value of the sum of the lengths of
its diagonals?

a. &#8730;8
b. 2&#8730;6
c. 2&#8730;10
d. 8
e. 10
Lets take a rectangle with sides 1 & 3 the diagonal must be equal to sqrt(1^2 + 3^2) or sqrt(10) since it's asking for the sum of the diagonals and the diagonals must be the same it would be 2 sqrt(10)

c.

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by mikeCoolBoy » Tue May 12, 2009 6:47 am
IMO B

Given an area the square has the smallest perimeter and therefore it has the smallest diagonal. The side of the square is 3^1/2 since the area is 3.

Diagonal = 2^(1/2) x 3^(1/2) = 6 ^(1/2)
The two diagonals account for = 2 x 6 ^(1/2)

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by marcusking » Tue May 12, 2009 6:52 am
mikeCoolBoy wrote:IMO B

Given an area the square has the smallest perimeter and therefore it has the smallest diagonal. The side of the square is 3^1/2 since the area is 3.

Diagonal = 2^(1/2) x 3^(1/2) = 6 ^(1/2)
The two diagonals account for = 2 x 6 ^(1/2)
I thought about it as a square too but my experience is that the GMAT is usually pretty straight forward about when it wants you to think of something as a square vs a rectangle. Would they be that tricky?

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