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Register now and save up to $200 Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## What is the perimeter? tagged by: Brent@GMATPrepNow This topic has 1 expert reply and 2 member replies phanikpk Senior | Next Rank: 100 Posts Joined 06 Jun 2014 Posted: 66 messages Followed by: 1 members #### What is the perimeter? Wed Jun 25, 2014 3:17 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) If the area of triangular region RST is 25. What is the perimeter of RST? 1) THe length of one of the sides is 5(2)^1/2 2) The triangle is a right isoceles triangle I have kept D, anyways B is only sufficient. The only way A is sufficient I thought is, since area has to be 25, the side whatever is given cannot be hypotenuse because, if side is 5(2)^1/2, then only we can get 25. If the given triangle is not right triangle the option A cannot hold true. If the question has a diagram depicting a right triangle then the answer can be D or not? Please help... Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8722 messages Followed by: 461 members Thanked: 2750 times GMAT Score: 800 Wed Jun 25, 2014 5:34 pm Hi phanikpk, I'm going to give you a hint so that you can continue working on this question. The prompt DOES NOT tell us that the triangle is a right triangle. NEITHER does Fact 1. You're assuming that it's a right triangle, BUT is it POSSIBLE that it's not? GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Thanked by: phanikpk ### Top Member GMATinsight Legendary Member Joined 10 May 2014 Posted: 998 messages Followed by: 21 members Thanked: 203 times Thu Jun 26, 2014 8:55 am Quote: If the area of triangular region RST is 25. What is the perimeter of RST? 1) THe length of one of the sides is 5(2)^1/2 2) The triangle is a right isosceles triangle Statement 1: Case 1: 5(Sqrt2) is Height of a right angle triangle other Sides will be 5(sqrt2) and 10 leading to perimeter = 10 + 10(sqrt2) Case 2: 5(Sqrt2) is Height of a NON-right angle triangle with base 5(sqrt2) Three sides will NOT be 5(sqrt2),5(sqrt2) and 10 leading to perimeter something other than 10 + 10sqrt2 Inconsistent result therefore, INSUFFICIENT STATEMENT Statement 2: The Isosceles right angle triangle with area 25 will essentially have sides as 5(sqrt2),5(sqrt2) and 10 therefore perimeter = 10+2x5sqrt2 = 10(1+sqrt2) SUFFICIENT Answer Option : B _________________ Prosper!!! Bhoopendra Singh & Sushma Jha "GMATinsight" Contact Us Testimonials To register for One-on-One FREE ONLINE DEMO Class Call/e-mail e-mail: info@GMATinsight.com Mobile: +91-9999687183 / +91-9891333772 Get in touch for SKYPE-Based Interactive Private Tutoring One-On-One Classes fee - US$40 per hour &
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Brent@GMATPrepNow GMAT Instructor
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Fri Jun 27, 2014 5:38 pm
phanikpk wrote:
If the area of triangular region RST is 25. What is the perimeter of RST?

1) The length of one of the sides is 5√2
2) The triangle is a right isosceles triangle

VERY IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

This technique can save a lot of time.

Target question: What is the perimeter of RST?

Given: The area of triangular region RST is 25.

Statement 1: The length of one of the sides is 5√2
There are several possible triangles such that the length of one side is 5√2. Here are two:

Notice that the perimeter for each triangle is DIFFERENT. In other words, statement 1 does not lock our shape into having just one perimeter.
As such, statement 1 is NOT SUFFICIENT

Statement 2: The triangle is a right isosceles triangle
This fact alone forces the triangle into having a 90-degree angle, 2 equal angles and 2 equal sides. Of course there still many different triangles (with different perimeters) that meet these conditions:

HOWEVER, it is given that the area of the triangle is 25. Among the infinite number of isosceles right triangles, ONLY ONE has an area of 25.
So, statement 2 (along with the given information) "locks" our triangle into ONE and ONLY ONE shape, which means there's only one possible perimeter.
As such, statement 2 is SUFFICIENT.
IMPORTANT: Need we actually find the perimeter of this triangle? No. We need only recognize that we COULD find the perimeter (if we so inclined to do so)

Cheers,
Brent

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