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

It is currently 11 Nov 2019, 12:51

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

In triangle ABC to the right, if BC = 3 and AC = 4, then what is the

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58954
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 02 Jun 2015, 06:33
1
sheolokesh wrote:
Hi Bunuel,

please explain me the correlation between 30-60-90(1:sq(3):2), 45-45-90(1:1:sq(2)) with pythagorean triplets(3-4-5, 7-24-25). I am confused because if we have a 90deg triangle, and 2 sides 3,4 we can put other side as 5? If so then it becomes 30-60-90 triangle right? then why we are not able to correlate 1:sq(3):2 with 3:4:5?
because we need to commonly multiply the ratio, so if 1*3 then sq(3) must also multiply by 3 which is not equal to 4..

Because I had tried an another approach which gives a wrong ans... Need clarification.. If ABC is a right triangle with 3,4 then other side must be 5. So Angle BAC will be 30 deg. which makes Ang CAD as 60 and CDA as 30.. So we have 30-60-90 triangle on ACD. If thats the case, then CD must be 4*sqrt(3) right? what's wrong in my approach?

Please help..


sheolokesh wrote:
if we have a 90deg triangle, and 2 sides 3,4 we can put other side as 5


Yes. If 3 and 4 are legs of a right triangle, then hypotenuse is 5.

sheolokesh wrote:
If so then it becomes 30-60-90 triangle right?


No. The angles in 3-4-5 right triangle are NOT 30°-60°-90°. They are ~53° - ~37 ° - 90°.
_________________
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 72
GMAT ToolKit User
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 02 Jun 2015, 07:00
So all triplets has 37-53-90 degrees right? Its better not to confuse triplets with 30-60-90 or 45-45-90 then..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58954
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 02 Jun 2015, 07:07
Intern
Intern
avatar
B
Joined: 17 Sep 2016
Posts: 3
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 11 Oct 2016, 09:37
Hey Could any one please tell me if my approach is correct! I used trigonometry!

Approach below:
Consider triangle ABC
cosθ = 3/5 (base/hyp)........(1)
Consider triangle ABD
cosθ = 5/(3+CD).........(2)

Equate (1) and (2)

3/5=5/(3+CD)
3CD+9= 25 ====> CD=16/3
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 11 Oct 2016, 11:24
Quote:
In triangle ABC, if BC = 3 and AC = 4, then what is the length of segment CD?

A. 3
B. 15/4
C. 5
D. 16/3
E. 20/3


As depicted in the figure, AB^2 = 3^2 + 4^2 = 5^2
i.e. AB = 5

NOW TRIANGLE ABC AND TRIANGLE ACD ARE SIMILAR TRIANGLE

So the ratio of their corresponding sides will be equal

AC/BC = CD/AC

4/3 = CD/4

i.e. CD = 16/3

Answer: option D
Attachments

File comment: www.GMATinsight.com
Sol1.jpg
Sol1.jpg [ 25.87 KiB | Viewed 11244 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
avatar
Joined: 22 Sep 2018
Posts: 1
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 30 Sep 2018, 02:24
How the angle BAC is equal to angle ADC
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 30 Sep 2018, 05:38
sudhanshutiwari wrote:
How the angle BAC is equal to angle ADC


sudhanshutiwari
Take bigger triangle ABD and mark Angles as 90-x - (90-x)

Now look at triangle ACD, one of the angle you can already see marked is (90-x) one angle is 90 so third angle becomes x (if you subtract other two angles from 180)

Similarly, look at triangle ABC, one of the angle you can already see marked is x one angle is 90 so third angle becomes 90-x (if you subtract other two angles from 180)

This is how, we figure out that angle BAC is equal to angle ADC

I hope this helps
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9764
Location: Pune, India
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the  [#permalink]

Show Tags

New post 24 Jun 2019, 04:59
VeritasKarishma wrote:
Both smaller triangles are similar to the large triangle. So they are similar to each other too.

In triangles BAD and BCA,
Angle BAD = BCA (90 degrees)
and angle B is common in both
So by AA, triangles BAD and BCA are similar

Similarly, in triangles BAD and ADC,
angle BAD = ACD (90 degrees)
and angle D is common in both
So by AA, triangles BAD and ACD are similar

So triangle BAD is similar to triangle BCA and ACD so triangle BCA is similar to triangle ACD too.


Responding to a pm:
Quote:
Can you explain why it's not BCA is similar to DCA? Since according to the image, A is the same for both triangles and C is the same, so shouldn't it be BCA and DCA?


Note that angles BCA and DCA are both 90 degrees so that's fine but angles BAC and DAC are not equal. These are two distinct angles and can take any values. Using the logic I have discussed in my solution, we find that triangle BCA is similar to triangle ACD.
_________________
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 >
GMAT Club Bot
Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the   [#permalink] 24 Jun 2019, 04:59

Go to page   Previous    1   2   [ 28 posts ] 

Display posts from previous: Sort by

In triangle ABC to the right, if BC = 3 and AC = 4, then what is the

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





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