Geometry

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VenugopalGurram: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Nov 29, 2012 12:55 am

by VenugopalGurram » Wed Dec 05, 2012 11:43 pm

x,2x and 3x are angles of the triangle, and the area of the triangle ABC=48 sq Units.What are the area of the triangles ABD and BDC?

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Source: Beat The GMAT — Quantitative Reasoning | Wed Dec 05, 2012 11:43 pm

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Thu Jan 17, 2013 10:32 am

They will both be 24. You will not have to use this application of angles on the GMAT, though.

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Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » Fri Jan 18, 2013 6:47 pm

Hey Guys,

Just wanted to weigh in on this. This particular geometry issue IS tested on the GMAT. It's actually just the rule that equal sides are opposite equal angles.

Because Triangle BCD is an equilateral triangle, all the sides are the same (BD=BC=CD). Next, because Angle A = Angle B, AD = BD, which means AD = DC.

That means the two triangles (ABD and BDC) have the same base (AD and DC) and the same height. So their areas are equal.

-t

P.S. To see the actual GMAT play with this trick, see Question 123 from the second edition of the Quant Official Guide.

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BTG14: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Fri Apr 06, 2012 5:28 amFollowed by: 2 members; Thanked: 3 times; GMAT Score:500

by BTG14 » Fri Jan 25, 2013 9:09 pm

Hi Tommy,

Did you conclude AD = BD because opposite angles are equal and in same way did you conclude AD=DC

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Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » Fri Jan 25, 2013 10:39 pm

Hey BTG,

That's absolutely right! Do the follow-up steps make sense to you?

-t

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