Triangle PS

Question

Triangle PS

justchill · Answer

answer is (7 sqrt 3)/4 and hence answer is B.

justchill · Answer

Area of total triangle:

Height = (3 * sqrt 3)/2
Base = 3

therefor area = (Height * Base)/2 = (9 * sqrt 3)/4.

Area of small triangle: sqrt 3/2

Therefore.

prash_c · Answer

how is area of smaller triangle sqrt(3/2).

TeHCM · Answer

Question implies that the triangle is an equalateral triangle. Therefore, the smaller triangle's degrees are 90-60-30. 

We know AB is 1, BE must be sqrt 3 and AE is 2.

Area = (AB*BE)/2 = sqrt 3/2

srinivasssrk · Answer

if you do not know how to solve the problem, don't worry, you can easily eliminate answers C, D and E as below:

Note that triangle ACD is equivilateral with side = 3.

The area of an equivilateral triangle is 1/4 (sqrt3)) * a * a where a is the side. in the current problem a = 3.

Hence, area of triangle (bigger triangle) is 1/4 (sqrt(3)) * 3 * 3 = 9/4 sqrt(3).

Since the quadrilateral BCDE is smaller (compared to ACD) in area, the answer should be less than 9/4 sqrt(3) (which you see is about 2 times sqrt(3)). and hence, answer C is eliminated right away.

Answer D is in fact more than 3 times (sqrt(3)), hence, is definitely more than Answer C, and hence is not a possible answer.

Similarly, answer E is 6+sqrt(3) can be written as 2 (sqrt3) (sqrt3) + sqrt(3) = (2sqrt(3)+1) sqrt(3), which is more than (2+1)sqrt(3), i.e. 3(sqrt3) and hence is more than answer C. Hence E is also not a possible answer.

Hence, pick between A and B. (increases your odds when you are guessing).

-Srinivas (mathguru).

Triangle PS

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards