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ABC and AED are triangles with BC parallel to ED. Find the a

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ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post 11 Oct 2013, 02:42
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ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Attachment:
Triangle_Barrons.png
Triangle_Barrons.png [ 45.21 KiB | Viewed 635 times ]


(1) BC = 8
(2) ED = 5
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Oct 2013, 02:43, edited 1 time in total.
Renamed the topic and edited the question.
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Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post 11 Oct 2013, 02:56
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ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Image

(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \frac{x}{y}, then their areas are in the ratio \frac{x^2}{y^2}.
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \frac{AREA}{area}=\frac{SIDE^2}{side^2}.

Since BC/ED=8/5, then \frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}. As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Manager
Manager
avatar
Joined: 06 Feb 2013
Posts: 60
Followers: 1

Kudos [?]: 5 [0], given: 33

Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post 14 Oct 2013, 03:41
Bunuel wrote:
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Image

(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \frac{x}{y}, then their areas are in the ratio \frac{x^2}{y^2}.
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \frac{AREA}{area}=\frac{SIDE^2}{side^2}.

Since BC/ED=8/5, then \frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}. As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.


Wonderfully done - one question please: "the area of ABC is 16" (in the stimulus) - is there anything we can infer from this information? Or does this information help us in any way before looking at S1 and S2?

_________________

There are times when I do not mind kudos...I do enjoy giving some for help

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18696
Followers: 3236

Kudos [?]: 22266 [1] , given: 2602

Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post 14 Oct 2013, 03:44
1
This post received
KUDOS
Expert's post
obs23 wrote:
Bunuel wrote:
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Image

(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \frac{x}{y}, then their areas are in the ratio \frac{x^2}{y^2}.
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \frac{AREA}{area}=\frac{SIDE^2}{side^2}.

Since BC/ED=8/5, then \frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}. As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.


Wonderfully done - one question please: "the area of ABC is 16" (in the stimulus) - is there anything we can infer from this information? Or does this information help us in any way before looking at S1 and S2?


We just know that the area is 16, we can get nothing more from it.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: ABC and AED are triangles with BC parallel to ED. Find the a   [#permalink] 14 Oct 2013, 03:44
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ABC and AED are triangles with BC parallel to ED. Find the a

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