GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Apr 2019, 18:57

### 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

# What is the area of triangle ABC ?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Oct 2012
Posts: 11
What is the area of triangle ABC ?  [#permalink]

### Show Tags

Updated on: 23 Jun 2015, 23:07
3
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:51) correct 43% (01:54) wrong based on 170 sessions

### HideShow timer Statistics

Attachment:

Untitled.png [ 24.36 KiB | Viewed 6780 times ]
What is the area of triangle ABC ?

(1) Side DC = 20

(2) Side AC = 8

Hi,

In the explanation of this question, it's telling me that the two angles at C are the same and therefore, the triangles are similar. But i'm not understanding why, how do we know thse two angles are equal?

Originally posted by yvette726 on 21 Feb 2014, 08:12.
Last edited by Bunuel on 23 Jun 2015, 23:07, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

21 Feb 2014, 09:08
3
4

What is the area of triangle ABC ?

Angle ACE is a straight line, hence it's 180°. Now, since (angle BCD)=90°, then (angle ACB) + (angle DCE) = 180° - 90° = 90°.

Next, in triangle ABC, (angle ACB) + (angle ABC) = 90°. Thus we have that:
(angle ACB) + (angle ABC) = 90° = (angle ACB) + (angle DCE) --> (angle ABC) = (angle DCE), which on the other hand implies that (angle ACB) = (angle CDE).

Therefore, all three angles in triangles ABC and CDE are equal, so these triangles are similar.

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: $$\frac{AREA}{area}=\frac{SIDE^2}{side^2}$$.

(1) Side DC = 20 --> $$CE=\sqrt{20^2-16^2}=12$$ --> $$AC=20-12=8$$ --> $$\frac{AREA_{CDE}}{area_{ABC}}=\frac{16^2}{8^2}$$. Since the area of triangle CDE = 16*12/2 = 96, then $$\frac{96}{area_{ABC}}=\frac{16^2}{8^2}$$ --> we can find the area od triangle ABC. Sufficient.

(2) Side AC = 8. The same info as above. Sufficient.

Below image might help to understand better:
Attachment:

Untitled.png [ 24.88 KiB | Viewed 5573 times ]

_________________
##### General Discussion
Intern
Joined: 01 Sep 2012
Posts: 8
Location: United States
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

21 Feb 2014, 09:35
Thank you Bunuel ! Superb explanation.
Current Student
Joined: 12 Aug 2015
Posts: 2613
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

31 Mar 2016, 19:54
Bunuel wrote:

What is the area of triangle ABC ?

Angle ACE is a straight line, hence it's 180°. Now, since (angle BCD)=90°, then (angle ACB) + (angle DCE) = 180° - 90° = 90°.

Next, in triangle ABC, (angle ACB) + (angle ABC) = 90°. Thus we have that:
(angle ACB) + (angle ABC) = 90° = (angle ACB) + (angle DCE) --> (angle ABC) = (angle DCE), which on the other hand implies that (angle ACB) = (angle CDE).

Therefore, all three angles in triangles ABC and CDE are equal, so these triangles are similar.

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: $$\frac{AREA}{area}=\frac{SIDE^2}{side^2}$$.

(1) Side DC = 20 --> $$CE=\sqrt{20^2-16^2}=12$$ --> $$AC=20-12=8$$ --> $$\frac{AREA_{CDE}}{area_{ABC}}=\frac{16^2}{8^2}$$. Since the area of triangle CDE = 16*12/2 = 96, then $$\frac{96}{area_{ABC}}=\frac{16^2}{8^2}$$ --> we can find the area od triangle ABC. Sufficient.

(2) Side AC = 8. The same info as above. Sufficient.

Below image might help to understand better:
Attachment:
Untitled.png

Hey I have a question here you mentioned ABC is similar to CDE
But i think the rotation specified here is incorrect
i think ABC is similar to ECD
Am i understanding this correctly ?
Would really appreciate you being more responsive
regards
S.C.S.A
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7589
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

31 Mar 2016, 20:26
1
Chiragjordan wrote:
Bunuel wrote:

What is the area of triangle ABC ?

Angle ACE is a straight line, hence it's 180°. Now, since (angle BCD)=90°, then (angle ACB) + (angle DCE) = 180° - 90° = 90°.

Next, in triangle ABC, (angle ACB) + (angle ABC) = 90°. Thus we have that:
(angle ACB) + (angle ABC) = 90° = (angle ACB) + (angle DCE) --> (angle ABC) = (angle DCE), which on the other hand implies that (angle ACB) = (angle CDE).

Therefore, all three angles in triangles ABC and CDE are equal, so these triangles are similar.

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: $$\frac{AREA}{area}=\frac{SIDE^2}{side^2}$$.

(1) Side DC = 20 --> $$CE=\sqrt{20^2-16^2}=12$$ --> $$AC=20-12=8$$ --> $$\frac{AREA_{CDE}}{area_{ABC}}=\frac{16^2}{8^2}$$. Since the area of triangle CDE = 16*12/2 = 96, then $$\frac{96}{area_{ABC}}=\frac{16^2}{8^2}$$ --> we can find the area od triangle ABC. Sufficient.

(2) Side AC = 8. The same info as above. Sufficient.

Below image might help to understand better:
Attachment:
Untitled.png

Hey I have a question here you mentioned ABC is similar to CDE
But i think the rotation specified here is incorrect
i think ABC is similar to ECD
Am i understanding this correctly ?
Would really appreciate you being more responsive
regards
S.C.S.A

Hi,

If you see the highlighted portion, Bunuel writes these triangles, no notation is given, are similar ...
Yes, it is always better to write the rotation of triangle as per the similarity of angles..
In this particular case, triangle ABC is similar to triangle ECD...

But finally we should look at the question and decide which angles are equal
_________________
Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

08 Sep 2017, 18:22
yvette726 wrote:
Attachment:
Untitled.png
What is the area of triangle ABC ?

(1) Side DC = 20

(2) Side AC = 8

Hi,

In the explanation of this question, it's telling me that the two angles at C are the same and therefore, the triangles are similar. But i'm not understanding why, how do we know thse two angles are equal?

Bunuel is it safe to say as a universal truth, on the GMAT, that if you know the hypotenuse of a right triangle AND the length of one other side then you know the length of the other side? I feel obviously yes but just want to make sure.
Math Expert
Joined: 02 Aug 2009
Posts: 7589
Re: What is the area of triangle ABC ?  [#permalink]

### Show Tags

08 Sep 2017, 20:08
Nunuboy1994 wrote:
yvette726 wrote:
Attachment:
Untitled.png
What is the area of triangle ABC ?

(1) Side DC = 20

(2) Side AC = 8

Hi,

In the explanation of this question, it's telling me that the two angles at C are the same and therefore, the triangles are similar. But i'm not understanding why, how do we know thse two angles are equal?

Bunuel is it safe to say as a universal truth, on the GMAT, that if you know the hypotenuse of a right triangle AND the length of one other side then you know the length of the other side? I feel obviously yes but just want to make sure.

Hi..

Yes, if you know any two sides in a right angle triangle, you can find the third side.
Also if you are given two sides of any triangle with the angle in between them, you can find the third side
_________________
Re: What is the area of triangle ABC ?   [#permalink] 08 Sep 2017, 20:08
Display posts from previous: Sort by