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The figure above shows four pieces of tile that have been

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The figure above shows four pieces of tile that have been [#permalink] New post 19 Jun 2007, 21:38
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A
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E

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The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?

(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.
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Re: DS - Sqaure [#permalink] New post 19 Jun 2007, 22:38
[quote="Amit05"]The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?

(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.[/quote]

Stmt 1 is SUFFICIENT. So A.

Consider the trapeziums BQSA and APRD. They have same area. Since three sides are given to be equal, the fourth side must also be equal.
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 [#permalink] New post 19 Jun 2007, 23:54
St1:
BQSA and APRD are similar rhombuses. So SQ should be = PR. Sufficinet

St2:
useless

Ans A
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 [#permalink] New post 20 Jun 2007, 09:39
Still cant understand how to interpret stmt 1. I seem to get E. Can someone explain stmt 1 in detail plz ?
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 [#permalink] New post 20 Jun 2007, 12:27
dahcrap wrote:
Still cant understand how to interpret stmt 1. I seem to get E. Can someone explain stmt 1 in detail plz ?


Ok .. This is how it is. Very simple. I was so dump not to get it..

We want to see if Given info is suff to prove QS = PR.

Let us take BQSA & PADR.

St 1 : BQ = CR = DG = AP

BQ = PA (St 1)
BA = AD (Sides of a sqare.. )
RD = CD-CR
AS = AD - SD.

But CR = SD (St 1)
AD = CD (Sides of a sqare.. )

hence RD = AS.

3 sides are congruent => 4th Side is Congruent.. Hence St 1 is sufficeint..

Hope this helps..

Caveat : Can we say if 3 sides of 2 quadrilateral are congruent then they are congruent. Could someone point me to some references.
  [#permalink] 20 Jun 2007, 12:27
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