Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

We know the larger and smaller triangles are similar, because they share the angle at P, and one other angle in each is 70º. What’s tricky is that they have different orientations, so that side PT actually corresponds to side PR. We know PR:PT = 3, so that’s the scale fact. Every length in triangle PRS is three times more than the corresponding side in triangle PTQ. If lengths are multiplied by 3, area is multiplied by 3 squared, or 9. Let’s say that the area of triangle PTQ is A. Then the area of triangle PRS is 9A. The shaded area is the difference of the two triangle areas, or 8A. If 8A = 48, this means A = 6, and that’s the area of triangle PTQ.

Well, PT = 4 is a base of PTQ, and QW is a corresponding altitude: call its length h.

Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and [#permalink]

Show Tags

23 Mar 2015, 03:01

It is probably worth mentioning that formula of 1/2*a*b*sin(a^b) is a good way to remember the relation between sides and the areas of triangles: as in, 1/2*PQ*PT*sin(P)/(1/2*PS*PR*sin(P) = PQ*PT/(PS*PR) = PQ*PT/(3*PQ*3*PT) = 1/3*1/3 = 1/9 in our case.

Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and [#permalink]

Show Tags

19 Feb 2016, 19:26

oh man..took me some time to solve..would definitely not solve on the actual test..spent about 10 minutes to solve it... we know that angles PTQ and QRS are 70 degrees. we also know that angle P is shared by the triangle PQT and PRS. since these 2 triangles have 2 similar angles, the triangles must be similar. the "base", or the segment from the 70 degree angle to the P angle is 3 times greater than PT, thus, the height of the PRS triangle must be 3 times greater than QW.

ok, so the area of the shaded region is: A(PRS)-A(PQT) = 48 area of PQT=4QW/2 = 2QW area of PRS=12*3QW/2 = 18QW.

Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and [#permalink]

Show Tags

08 Sep 2017, 08:16

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________