GRE Prep Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the figure above, DE is parallel to AC. BE = 2EC DE = 12
[#permalink]
26 Sep 2018, 15:03
26 Sep 2018, 15:03
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
51% (01:11) correct
48% (01:16) wrong based on 90 sessions
Hide Show timer Statistics
Attachment:
Capture.JPG [ 11.69 KiB | Viewed 9150 times ]
In the figure above, DE is parallel to AC.
BE = 2EC
DE = 12
Quantity A |
Quantity B |
AC |
18 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: In the figure above, DE is parallel to AC. BE = 2EC DE = 12
[#permalink]
12 Aug 2019, 21:10
12 Aug 2019, 21:10
1
1
Bookmarks
Since, DE and AC are parallel , we can say that the inner (smaller) triangle is a fraction of the outer triangle and ratios of each corresponding sides of the triangles are equal
Therefore we can write , BE/BC = DE/AC
=> 2EC/3EC = 12/AC
=> 2AC = 36
=> AC = 18
Answer is C
Therefore we can write , BE/BC = DE/AC
=> 2EC/3EC = 12/AC
=> 2AC = 36
=> AC = 18
Answer is C
Re: In the figure above, DE is parallel to AC. BE = 2EC DE = 12
[#permalink]
09 Nov 2019, 01:11
09 Nov 2019, 01:11
2
Bookmarks
Official Explanation
If AC is parallel to DE, then triangles DBE and ABC are similar. If BE = 2EC then if EC is set to equal x, BE would equal 2x and BC would equal x + 2x, or 3x. That means that the big triangle is in a 3 : 2 ratio with the small triangle (since BC : BE = 3x : 2x). Set up the proportion for the bottom sides of these triangles, both of which are opposite the shared vertex at B:
\(\frac{2}{3}\) = \(\frac{DE}{AC}\)
\(\frac{2}{3}\)= \(\frac{12}{AC}\)
2(AC) = 36
AC = 18
The two quantities are equal.
If AC is parallel to DE, then triangles DBE and ABC are similar. If BE = 2EC then if EC is set to equal x, BE would equal 2x and BC would equal x + 2x, or 3x. That means that the big triangle is in a 3 : 2 ratio with the small triangle (since BC : BE = 3x : 2x). Set up the proportion for the bottom sides of these triangles, both of which are opposite the shared vertex at B:
\(\frac{2}{3}\) = \(\frac{DE}{AC}\)
\(\frac{2}{3}\)= \(\frac{12}{AC}\)
2(AC) = 36
AC = 18
The two quantities are equal.
