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# A square with diagonal 10*2^(1/2) and a rectangle both have sides with

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Math Expert
Joined: 02 Sep 2009
Posts: 58443
A square with diagonal 10*2^(1/2) and a rectangle both have sides with  [#permalink]

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23 Aug 2018, 03:54
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Difficulty:

15% (low)

Question Stats:

94% (01:06) correct 6% (00:20) wrong based on 21 sessions

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A square with diagonal $$10\sqrt{2}$$ and a rectangle both have sides with integer lengths. If the area of the square is equal to the area of the rectangle, which of the following cannot be a side of the rectangle?

A. 2
B. 5
C. 10
D. 40
E. 50

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Re: A square with diagonal 10*2^(1/2) and a rectangle both have sides with  [#permalink]

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23 Aug 2018, 04:04
Bunuel wrote:
A square with diagonal $$10\sqrt{2}$$ and a rectangle both have sides with integer lengths. If the area of the square is equal to the area of the rectangle, which of the following cannot be a side of the rectangle?

A. 2
B. 5
C. 10
D. 40
E. 50

A square with diagonal $$10\sqrt{2}$$

Side is 10 hence Area of square =100

Except D=40, All can be sides of the rectangle
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Re: A square with diagonal 10*2^(1/2) and a rectangle both have sides with  [#permalink]

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23 Aug 2018, 07:43
Bunuel wrote:
A square with diagonal $$10\sqrt{2}$$ and a rectangle both have sides with integer lengths. If the area of the square is equal to the area of the rectangle, which of the following cannot be a side of the rectangle?

A. 2
B. 5
C. 10
D. 40
E. 50

Sides of the square = 10 ( As Diagonal of the square = $$a\sqrt{2}$$)

Area of the square = Area of the Rectangle = 100

As the products of the 2 sides of a rectangle = 100 , the other side must be a factor of 100

Among the given options all except (D) is a factor of 100 , Hence Anwer must be (D)
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Re: A square with diagonal 10*2^(1/2) and a rectangle both have sides with  [#permalink]

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26 Aug 2018, 19:17
Bunuel wrote:
A square with diagonal $$10\sqrt{2}$$ and a rectangle both have sides with integer lengths. If the area of the square is equal to the area of the rectangle, which of the following cannot be a side of the rectangle?

A. 2
B. 5
C. 10
D. 40
E. 50

The side of the square is 10, so the area is 100.

Thus:

100 = L x W

Since 40 is not a factor of 100, 40 cannot be a side of the rectangle.

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Re: A square with diagonal 10*2^(1/2) and a rectangle both have sides with   [#permalink] 26 Aug 2018, 19:17
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