GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
In triangle ABC shown above, if BC = 3 and AC = 4, then what is the
[#permalink]
31 Mar 2021, 09:20
31 Mar 2021, 09:20
Expert Reply
3
Bookmarks
00:00
Question Stats:
60% (02:15) correct
40% (02:00) wrong based on 5 sessions
Hide Show timer Statistics
Attachment:
Triangle.jpg [ 3.83 KiB | Viewed 4118 times ]
In triangle ABC shown above, 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
In triangle ABC shown above, if BC = 3 and AC = 4, then what is the
[#permalink]
31 Mar 2021, 21:10
31 Mar 2021, 21:10
1
To find CD, we can find BD and reduce BC from it.
In the right angled triangle ABC, AB = 5 since BC = 3 and AC = 4.
Applying theory of similarity of triangles
The triangles ABC and ABD must be similar since both triangles have equal angles. Angle ABC = angle ABD, angle ACB = angle BAD, and angle BAC = angle ADB. The sides of both triangles will be in a fixed ratio corresponding to their angles.
\(\frac{AB}{BD }=\frac{ BC}{AB}\)
\(\frac{5}{BD} = \frac{3}{5}\)
\(BD = \frac{25}{3}\)
\(CD = BD - BC = \frac{25}{3} - 3 = \frac{16}{3}\).
D is the correct answer.
In the right angled triangle ABC, AB = 5 since BC = 3 and AC = 4.
Applying theory of similarity of triangles
The triangles ABC and ABD must be similar since both triangles have equal angles. Angle ABC = angle ABD, angle ACB = angle BAD, and angle BAC = angle ADB. The sides of both triangles will be in a fixed ratio corresponding to their angles.
\(\frac{AB}{BD }=\frac{ BC}{AB}\)
\(\frac{5}{BD} = \frac{3}{5}\)
\(BD = \frac{25}{3}\)
\(CD = BD - BC = \frac{25}{3} - 3 = \frac{16}{3}\).
D is the correct answer.
gmatclubot
In triangle ABC shown above, if BC = 3 and AC = 4, then what is the [#permalink]
31 Mar 2021, 21:10
Moderators:
