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Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink]
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Welcome on board. :)

It is fine the way you have formatted.

Could be a bit better but is not the problem. Here we are to learn.

As long as you follow the rules for posting we are always eager to help the students.


Here a list of useful link on our community. Keep in mind that the relevant posts are put at the top of the general page (quant and verbal) or at the top of the specific page you wanna visit (say The sub forum quantitative comparison question)

How to post a question on the board and the use of the tag (very important)

Quant - https://gre.myprepclub.com/forum/how-to-po ... 12752.html
Verbal - https://gre.myprepclub.com/forum/how-to-po ... 12927.html

The rules of the board https://gre.myprepclub.com/forum/rules-for ... -1083.html

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All the Official Guides in one directory (of course from then follow the links ) https://gre.myprepclub.com/forum/the-offic ... -8020.html

All the PowerPrep (the free software Provided by ETS - who own the GRE) questions explained https://gre.myprepclub.com/forum/gre-power ... -3118.html

All the powerprep question explained for free in pdf by Skypetutor https://gre.myprepclub.com/forum/vince-and ... 12946.html

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Our main quant directory with the most relevant GRE books

Quant - https://gre.myprepclub.com/forum/the-last- ... -3523.html
Verbal - https://gre.myprepclub.com/forum/the-last- ... -3488.html

All you need to know about the GRE https://gre.myprepclub.com/forum/all-you-d ... -7924.html

Our guide for quantitative reasoning for the GRE exam https://gre.myprepclub.com/forum/the-defin ... -8898.html

The study plan for the 2019 https://gre.myprepclub.com/forum/gre-study ... -8885.html

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And last but not least our test https://gre.myprepclub.com/tests/

Hope this helps :)

Ask for further assistance.

PS: there are more resources here. Just take a look at the announcement/sticky posts or do a search via the search button https://gre.myprepclub.com/forum/search.php

Regards

Ask for further assistance I have attached the GC quant book that after ten years of experience I do think is the only thing to have for the quant concepts.

Practice at least one hour per day but not more than two first in your areas of content weak then consolidate the strongest areas.
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Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink]
Thank you for the response viktorIartav, but what if we do not want to use trigonometry? Is there another way?
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Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink]
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Trigonometry is not contemplated any more for the GRE exam.
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Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink]
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let us take the first parallelogram. PQRS
PQ = 2QR
Perimeter - 2(PQ+QR)=2(2QR+QR)=6QR=24......QR=4 and PQ=2*4=8
Now let us see the area of PQRS
drop a perpendicular from Q on PS -> QA
Now PQA is 30-60-90 triangle as angle PQT = 120-90=30..
so if PQ is 8, height or PA will be \(8\sqrt{3}/2=4\sqrt{3}\)
Thus area = PS*QA = \(4*4\sqrt{3}\)=\(16\sqrt{3}\)...

so area of parallelogram TQUV is \(16\sqrt{3}/2=8\sqrt{3}\)..
now let QU be a, so TQ=2a...
height of TQUV will be TQ*\(\sqrt{3}/2=a\sqrt{3}\), as TQA' is also 30-60-90.
thus its area = \(a*a\sqrt{3}=a^2\sqrt{3}=8\sqrt{3}\), so \(a=2\sqrt{2}\)..
thus perimeter is 2(a+2a)=6a=6*\(2\sqrt{2}=12*1.414=17\)
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Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink]
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