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# Does rectangle A have a greater perimeter that rectangle B?

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Manager
Joined: 24 Jun 2003
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Does rectangle A have a greater perimeter that rectangle B? [#permalink]  07 Aug 2003, 02:49
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Does rectangle A have a greater perimeter that rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B.
2) The area of rectangle A is twice the area of rectangle B.
Manager
Joined: 24 Jun 2003
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Location: India
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Re: DS practice # 6 [#permalink]  07 Aug 2003, 04:35
Konstantin Lynov wrote:
Does rectangle A have a greater perimeter that rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B.
2) The area of rectangle A is twice the area of rectangle B.

Let a and b be the sides of rectangle 1; x and y the corresponding sides of rectangle 2.

Perimeter is defined as 2*(a+b) for Rect 1 and 2*(x+y) for Rect 2

From (1) we only know that a=2x. This does not help us answer our question since the other side is unknown

(2) tells us that atleast one of the sides of Rect A is larger than the lenghts of the sides on Rect B. This means that the perimeter of A would be larger than the perimeter of B

SVP
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(2) consider a quadrilateral 2-2-2-2, its area is 4, its perimeter is 8
consider a rectangular 10-1/5-10-1/5, its area is 2, its perimeter is 20 and 2/5

consider a quadrilateral 2-2-2-2, its area is 4, its perimeter is 8
consider a rectangular 1-2-1-2, its area is 2, its perimeter is 6

So, B is clearly wrong.

Combine: ab=2cd and a=2c plug and get b=d -- sufficient. One side is common, another is twise as much as its counterpart.

C
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