Among all rectangles of area 3, what is the smallest possible value of the sum of the lengths of
its diagonals?
a. √8
b. 2√6
c. 2√10
d. 8
e. 10
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Do you know a Rectangle when you see one?
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marcusking
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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)dtweah wrote:Among all rectangles of area 3, what is the smallest possible value of the sum of the lengths of
its diagonals?
a. √8
b. 2√6
c. 2√10
d. 8
e. 10
c.
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mikeCoolBoy
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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)
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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marcusking
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- Joined: Wed Feb 04, 2009 6:09 am
- Location: Louisville, KY
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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?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)
