GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Feb 2020, 06:36

### 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

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

# If AD is 6 and ADC is a right angle, what is the area of triangular re

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

### Hide Tags

Manager
Joined: 19 Aug 2016
Posts: 70
If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

15 Oct 2017, 17:25
Bunuel wrote:

Given: $$AD=6$$. Question: $$area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?$$

(1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio $$1:\sqrt{3}:2$$ --> as AD=6 (larger leg opposite 60 degrees angle) then $$BD=\frac{6}{\sqrt{3}}$$ (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient.

(2) AC=12, we can find DC. But we still don't know BD. Not sufficient.

(1)+(2) We know both BD and DC, hence we can find area. Sufficient.

Hi Bunuel

Cant we assume that that AD bisects BC into two?

Please clear my doubt thanks
Math Expert
Joined: 02 Sep 2009
Posts: 61508
If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

15 Oct 2017, 20:36
zanaik89 wrote:
Bunuel wrote:

Given: $$AD=6$$. Question: $$area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?$$

(1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio $$1:\sqrt{3}:2$$ --> as AD=6 (larger leg opposite 60 degrees angle) then $$BD=\frac{6}{\sqrt{3}}$$ (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient.

(2) AC=12, we can find DC. But we still don't know BD. Not sufficient.

(1)+(2) We know both BD and DC, hence we can find area. Sufficient.

Hi Bunuel

Cant we assume that that AD bisects BC into two?

Please clear my doubt thanks

No. The height and the median coincide only in isosceles/equilateral triangle, when the height is dropped from the vertex formed by equal sides to the base.
_________________
Manager
Joined: 19 Aug 2016
Posts: 70
If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

16 Oct 2017, 01:46
zanaik89 wrote:

Given: $$AD=6$$. Question: $$area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?$$

(1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio $$1:\sqrt{3}:2$$ --> as AD=6 (larger leg opposite 60 degrees angle) then $$BD=\frac{6}{\sqrt{3}}$$ (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient.

(2) AC=12, we can find DC. But we still don't know BD. Not sufficient.

(1)+(2) We know both BD and DC, hence we can find area. Sufficient.

Hi Bunuel

Cant we assume that that AD bisects BC into two?

Please clear my doubt thanks[/quote]

So u mean that since it isnt given that triangle ABC is an isoceles triangle or equilateral triangle, we can not consider AD as a perpendicular bisector right?
Math Expert
Joined: 02 Sep 2009
Posts: 61508
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

16 Oct 2017, 01:53
zanaik89 wrote:

So u mean that since it isnt given that triangle ABC is an isoceles triangle or equilateral triangle, we can not consider AD as a perpendicular bisector right?

Yes, we know that AD is perpendicular to BC but we don't know whether it bisects BC.
_________________
Intern
Joined: 23 Jun 2018
Posts: 22
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

31 Aug 2018, 07:58
If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?[/b]

Given: $$AD=6$$. Question: $$area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?$$

(1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio $$1:\sqrt{3}:2$$ --> as AD=6 (larger leg opposite 60 degrees angle) then $$BD=\frac{6}{\sqrt{3}}$$ (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient.

(2) AC=12, we can find DC. But we still don't know BD. Not sufficient.

(1)+(2) We know both BD and DC, hence we can find the area. Sufficient.

Bunuel - My doubt is if a triangle like this which has a 30-60-90 angles, shouldn't the the triangle ADC should also be 30-60-90 making triangle ABC an equilateral triangle? because an equilateral triangle can be formed by joining two identical triangles, each with 30-60-90 angles.
Manager
Joined: 18 Feb 2018
Posts: 102
GMAT 1: 750 Q45 V41
GMAT 2: 750 Q50 V41
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

09 Jul 2019, 06:17
Bunuel VeritasKarishma The stem says that ADC is a right angle. That means AD is perpendicular to DC. Why are we assuming that B, D and C are in a straight line?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10119
Location: Pune, India
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

10 Jul 2019, 05:21
GittinGud wrote:
Bunuel VeritasKarishma The stem says that ADC is a right angle. That means AD is perpendicular to DC. Why are we assuming that B, D and C are in a straight line?

BC is a straight line and D lies on it. Note sure why you think right triangle ADC messes that up.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Joined: 18 Feb 2018
Posts: 102
GMAT 1: 750 Q45 V41
GMAT 2: 750 Q50 V41
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

10 Jul 2019, 07:47
VeritasKarishma We have no information in the stem to decide whether BC is a straight line. Why are we assuming it is?
Manager
Joined: 23 Jul 2015
Posts: 84
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

10 Jul 2019, 10:12
AccipiterQ wrote:

I thought if you dropped a line down from a triangle vertex and it formed a right angle on the opposite side then that line bisected the side? So in this case if you know what BD is then you know what DC is?

To figure out whether it holds, why don't you try drawing some extreme figures, say, something like this:
Attachment:
Ques3.jpg

Will this be true in this case?
When will it be true? When the triangle is equilateral, sure. Also when the triangle is isosceles if the equal sides form the angle from which the altitude is dropped.

Don't put your faith in the figure given. It may be just one of the many possibilities or may be somewhat misleading.

Hi! How do we know that the ADC is also a 90 30 60 triangle?
Senior Manager
Joined: 10 Aug 2018
Posts: 340
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

### Show Tags

03 Oct 2019, 02:33
Nice question with a good trap.
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re   [#permalink] 03 Oct 2019, 02:33

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by

# If AD is 6 and ADC is a right angle, what is the area of triangular re

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

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