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MGMAT CAT 1 - Similar triangles

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Anil
 Post subject: MGMAT CAT 1 - Similar triangles
 Post Posted: Fri Jun 27, 2008 2:42 am 
Hello,
can someone explain the conclusion underlined in RED (see attached image) ?

Consider triangle PQS -
given angle S = 90
if angle P = x
then angle PQS = 90 -x


and triangle QSR -
given angle S = 90
if angle R = y
then angle SQR = 90 -y

Nothing in the data leads to x = y OR x = 90 -y OR y = 90 -x

i.e. the inner triangles share only one common angle (the right angle) - then how are triangles PQS and QSR similar ? (or in other words, how are all three triangles similar ?)

In fact, the problem goes on to say that the ratio of the areas of triangles PQS and RQS are in the ratio of the square of the respective side lengths. That seems incorrect.

Consider,
area triangle PQS = 1/2 (PS)(QS)
area triangle QSR = 1/2 (SR)(QS)

so the areas are in the ratio = PS/SR, which is the ratio of respective side lengths, and not square of the respective side lengths. Should'nt the answer be 4/3 ?


Image
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Guest
 Post subject:
 Post Posted: Fri Jun 27, 2008 11:04 am 
On further thoughts,

angle PQS + SQR = 90
90 -x + 90 - y = 90
x + y = 90

So, x = 90 -y OR y = 90-x, which makes the triangles similar.

However, can someone explain the other question I had (ratio of areas) ? It still seems like the answer should be 4/3
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StaceyKoprince
 Post subject:
 Post Posted: Tue Jul 01, 2008 12:29 am 
Offline
ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
Quote:
area triangle PQS = 1/2 (PS)(QS)
area triangle QSR = 1/2 (SR)(QS)


The above is right. Go back and check the actual lengths of PS and SR. PS is 16 and SR is 9. :)

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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Anil
 Post subject:
 Post Posted: Tue Jul 01, 2008 4:00 pm 
Thanks Stacey. Should have seen that error.
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Guest
 Post subject: Values for PS and SR?
 Post Posted: Sat Jul 05, 2008 7:11 pm 
Hmm - I'm not seeing how the values of PS and SR are arrived - Please can someone help explain?
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Guest
 Post subject:
 Post Posted: Wed Jul 09, 2008 4:31 pm 
Anyone?
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Guest
 Post subject:
 Post Posted: Wed Jul 09, 2008 11:51 pm 
I ran into the same problem.


http://www.manhattangmat.com/forums/wei ... t3708.html
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Guest
 Post subject: thanks!
 Post Posted: Thu Jul 10, 2008 1:43 am 
Anonymous wrote:
I ran into the same problem.


http://www.manhattangmat.com/forums/wei ... t3708.html


Thank you!
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StaceyKoprince
 Post subject:
 Post Posted: Wed Sep 03, 2008 7:05 pm 
Offline
ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
thanks!

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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