Jul 23 10:00 PM PDT  11:00 PM PDT This period of time is long enough: it gives you more than enough time to comfortably learn, review and practice all of the material. On the other hand it is not too long. Jul 24 11:30 PM EDT  10:00 PM EDT Free GRE Class: First Session. Experience the power of live instruction, for free. Our sample classes showcase our passionate and dedicated faculty and the way they'll guide you through proven strategies for improving your score. Jul 25 07:00 PM EDT  08:00 PM EDT Strategies and techniques for approaching featured GRE topics. An introduction to one of Manhattan Prep’s GRE worldclass instructors. Jul 29 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and SchoolApply and learn how to ace the GRE & score higher and how to pick the right University for you. Save your spot today! Jul 29 10:00 PM PDT  11:00 PM PDT A Revolutionary OnDemand GRE Prep Course. Try for $1 Jul 30 10:00 PM PDT  11:00 PM PDT 7+ POINT GRE SCORE IMPROVEMENT GUARANTEE Jul 31 10:00 PM PDT  11:00 PM PDT Sign up for 1 Week GRE Prep
Author 
Message 
TAGS:


Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 18
Kudos [?]:
50
[0], given: 220

Triangle ABC is symmetric about the yaxis. Point A is locat [#permalink]
12 Nov 2017, 01:05
Question Stats:
80% (01:25) correct
20% (00:01) wrong based on 10 sessions
Triangle ABC is symmetric about the yaxis. Point A is located at (4,0), and AB is the longest side of ABC. If the perimeter of ABC is 18, what is the area? A. 3√2 B. 6 C. 6√2 D. 12 E. 24 Kudos for correct solution.




Director
Joined: 03 Sep 2017
Posts: 520
Followers: 1
Kudos [?]:
364
[1]
, given: 66

Re: Triangle ABC is symmetric about the yaxis. Point A is locat [#permalink]
13 Nov 2017, 00:07
1
This post received KUDOS
Since the triangle is symmetric with respect to axis y, one of its points, A, is (4, 0) and AB is the longest side, AB = 8. Then, given 18 is the perimeter, we can derive the length of the two other sides as being 5 and 5. Thus, focusing on one half of the triangle we can notice that it is rightangled and its sides are a Pythagorean triplet 345. Then, the height of the triangle is 3.
The area of ABC is then computed as (8*3)/2 = 12
Answer D



Intern
Joined: 27 Oct 2018
Posts: 49
Followers: 0
Kudos [?]:
15
[0], given: 27

Re: Triangle ABC is symmetric about the yaxis. Point A is locat [#permalink]
02 Nov 2018, 11:57
How to know AB = 8? Not given in the question



Intern
Joined: 27 Oct 2018
Posts: 49
Followers: 0
Kudos [?]:
15
[2]
, given: 27

Re: Triangle ABC is symmetric about the yaxis. Point A is locat [#permalink]
02 Nov 2018, 11:59
2
This post received KUDOS
Step #1 With coordinate geometry questions in which there is no coordinate plane, always make sure to draw the plane and any diagram (with practice, you’ll get quick at making a rudimentary version). Trying to visualize the information is simply much more difficult.
Step #2 Once you’ve drawn all the information, which should include Point A and B, then the next steps should be easier. By the way, point B is located at (4,0). Remember, ABC is symmetric about the yaxis, meaning that exactly half of the triangle is on the left side of the yaxis; the other half is on the right side. The only way to arrange such a triangle is to have AB as a horizontal line, which forms the base of the triangle.
If you don’t believe me try drawing a triangle in which AB is not a horizontal line and the triangle is symmetric about the yaxis.
Step #3 At this point, you may have also noticed that the triangle is an isosceles triangle (equal parts on both sides of the axis). Therefore the top of triangle is located on the yaxis. Whether it is above line AB or below doesn’t matter, as we are only looking for the area of ABC (the height will be constant—the distance point C is from side AB).
Step #4 Because we have an isosceles triangle, BC and AC must both equal 5. Remember the perimeter is 18. AB accounts for 8, leaving 10 for both sides. Splitting the triangle in half (basically each side of the triangle), we have two 3:4:5 right triangles. Therefore the height is 3, and the area of the triangle is 12, Answer (D).
Bonus Step: This problem could have been even more difficult had I not provided the information that AB is the longest side. In that case, we still would have had the exact same triangle. Point B and Point C could be switched, but that detail is moot because the dimensions of the triangle would have been exactly the same.




Re: Triangle ABC is symmetric about the yaxis. Point A is locat
[#permalink]
02 Nov 2018, 11:59





