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# Traingle DS.....

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Manager
Joined: 02 Sep 2008
Posts: 103

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06 Apr 2009, 01:23
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Director
Joined: 01 Apr 2008
Posts: 847
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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08 Apr 2009, 20:21
Notice that its a 30-60-90 triangle with p=90, r=60, t=30

From1) QRS is equilateral because r=60 and two sides are equal in length. Hence,angle RSQ=60. But we cant say anything about x until we know angle TSU.

From2) angle TSU = angle TUS = 30. We cant say anything about x until we know angle RSQ.

From 1 and 2, x = 180 - 60-30 =90

Hence, C.
Current Student
Joined: 13 Jan 2009
Posts: 352
Location: India

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13 Apr 2009, 20:20
Economist wrote:
Notice that its a 30-60-90 triangle with p=90, r=60, t=30

From1) QRS is equilateral because r=60 and two sides are equal in length. Hence,angle RSQ=60. But we cant say anything about x until we know angle TSU.

From2) angle TSU = angle TUS = 30. We cant say anything about x until we know angle RSQ.

From 1 and 2, x = 180 - 60-30 =90

Hence, C.

I am not sure how we can notice that...

St1: Since RQ=RS there fore, angle RQS=RSQ=a not suff.
St2: Since ST=TU there fore, angle UST=SUT=b not suff.

From triangle properties we know that angle R+P+T=180

so R+T+P=180
R+T=90
180-2a+180-2b=90
a+b=145

now a+b+x=180
so x=35

Hence C
Manager
Joined: 19 Aug 2006
Posts: 233

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14 Apr 2009, 19:26
hemantsood wrote:
Economist wrote:
Notice that its a 30-60-90 triangle with p=90, r=60, t=30

From1) QRS is equilateral because r=60 and two sides are equal in length. Hence,angle RSQ=60. But we cant say anything about x until we know angle TSU.

From2) angle TSU = angle TUS = 30. We cant say anything about x until we know angle RSQ.

From 1 and 2, x = 180 - 60-30 =90

Hence, C.

I am not sure how we can notice that...

St1: Since RQ=RS there fore, angle RQS=RSQ=a not suff.
St2: Since ST=TU there fore, angle UST=SUT=b not suff.

From triangle properties we know that angle R+P+T=180

so R+T+P=180
R+T=90
180-2a+180-2b=90
a+b=145

now a+b+x=180
so x=35

Hence C

I had the same reasoning. However, I think you made a small mistake (typo) - a+b=135, not 145, and as the result x=45.
Re: Traingle DS.....   [#permalink] 14 Apr 2009, 19:26
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