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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
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31 Mar 2021, 09:20
31 Mar 2021, 09:20
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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
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