It is currently 17 Oct 2017, 10:35

Close

GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure above, if AC = 18, what is the area of ∆ BCD?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128566 [1], given: 12180

In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 24 Aug 2017, 01:54
1
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

79% (00:56) correct 21% (01:27) wrong based on 53 sessions

HideShow timer Statistics

Image
In the figure above, if AC = 18, what is the area of ∆ BCD?

(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined

[Reveal] Spoiler:
Attachment:
2017-08-24_1249.png
2017-08-24_1249.png [ 7.77 KiB | Viewed 512 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128566 [1], given: 12180

Director
Director
User avatar
G
Joined: 18 Aug 2016
Posts: 511

Kudos [?]: 139 [0], given: 123

GMAT 1: 630 Q47 V29
GMAT ToolKit User Premium Member Reviews Badge
Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 24 Aug 2017, 02:51
Bunuel wrote:
Image
In the figure above, if AC = 18, what is the area of ∆ BCD?

(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined

[Reveal] Spoiler:
Attachment:
2017-08-24_1249.png


\(AB = \sqrt{100-64} = \sqrt{36} = 6\)
Area of ABC = 1/2 * 6 * 18 = 54
Area of ABD = 1/2 * 6 * 8 = 24
Area of BCD = 54-24 = 30

B
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Kudos [?]: 139 [0], given: 123

Manager
Manager
avatar
B
Joined: 14 Sep 2016
Posts: 136

Kudos [?]: 5 [0], given: 35

Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 24 Aug 2017, 05:00
Answer = B

AB^2 + 8^2 = 100

We get AB = 6

Area of triangle ABC - Area of triangle ABD = Area of triangle DBC

We get area = 30

Kudos [?]: 5 [0], given: 35

BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1449

Kudos [?]: 591 [0], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 24 Aug 2017, 05:10
Image

In right angled ∆BAD, AB \(= \sqrt{100 - 64} = \sqrt{36} = 6\)
The area of the ∆BAC = \(\frac{1}{2} * AB * AC = \frac{1}{2} * 6 * 18 = 54\)
The triangles have the same height, but their bases are in the ratio \(9:4(18:8)\)
Hence, the areas of the two triangles also have to be in the same ratio.

So the area of the ∆BCD must be \(\frac{9-4}{9}*54 = 30\)(Option B)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 591 [0], given: 16

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 799

Kudos [?]: 252 [0], given: 544

Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 24 Aug 2017, 13:09
Bunuel wrote:
Image
In the figure above, if AC = 18, what is the area of ∆ BCD?

(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined

[Reveal] Spoiler:
Attachment:
2017-08-24_1249.png

\(Area =
\frac{b*h}{2}\)


The height AB of ∆ BCD is the short leg of a 3-4-5 triangle, ∆ ABD.

Sides here have ratio of 6: 8: 10 (multiplier is x = 2, so 3x is 3*2 = 6)

If you are given a right triangle, and two of the three sides correspond with the 3x: 4x: 5x ratio, by definition the third side also corresponds.

Base CD of ∆ BCD is 10

AC - AD = CD
(18 - 8) = 10

\(\frac{(6 * 10)}{2}\) = 30

Answer B

Kudos [?]: 252 [0], given: 544

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1619

Kudos [?]: 835 [0], given: 2

Location: United States (CA)
Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]

Show Tags

New post 29 Aug 2017, 16:18
Bunuel wrote:
Image
In the figure above, if AC = 18, what is the area of ∆ BCD?

(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined


Since triangle ABD is a right triangle, we see that it’s a 6-8-10 right triangle with a height of 6. Thus, the area of triangle ABD is (8 x 6)/2 = 24.

Since triangle ABC is also a right triangle, the area of triangle ABC is [18 x 6]/2 = 54.

Since the area of triangle BCD is the difference between the areas of triangle ABC and triangle ABD, the area of triangle BCD is 54 - 24 = 30.

Alternate Solution:

We see that |DC| = |AC| - |AD| = 18 - 8 = 10. We also note that the height belonging to this base is the side AB, which is found to have a length of 6 from the ABD right triangle. Thus, the area of BCD is (10 x 6)/2 = 30.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 835 [0], given: 2

Re: In the figure above, if AC = 18, what is the area of ∆ BCD?   [#permalink] 29 Aug 2017, 16:18
Display posts from previous: Sort by

In the figure above, if AC = 18, what is the area of ∆ BCD?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.