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30 Dec 2020, 01:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:34) correct
17%
(01:26)
wrong
based on 66
sessions
History
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Which of the following are possible side lengths of triangle CDE ?
I. 6, 8, and 14
II. 8, 12, and 16
III. 16, 24, and 32
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Attachment:
1.png [ 24.02 KiB | Viewed 3432 times ]
30 Dec 2020, 02:07
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Triangle BCA is similar to Triangle CDE (By AA) Angle BAC = Angle EDC and Angle BCA = Angle DCE
The ratio of sides have to be equal. So \(\frac{AB}{DE} = \frac{BC}{CE} = \frac{AC}{CD}\), where DE is the smallest side, CE the second longest and CD is the longest.
Statement I: Sides are 6, 8, 14. Here AB / DE = 4/6 = 2/3 and BC/CE = 6/8 = 3/4. Therefore this is not possible.
Statement II: Sides are 8, 12, 16. Here AB / DE = BC/CE = AC/CD = 1/2. Therefore this is possible.
Statement III: Sides are 16, 24, 32. Here AB / DE = BC/CE = AC/CD = 1/4. Therefore this is possible.
Option D
Arun Kumar
The ratio of sides have to be equal. So \(\frac{AB}{DE} = \frac{BC}{CE} = \frac{AC}{CD}\), where DE is the smallest side, CE the second longest and CD is the longest.
Statement I: Sides are 6, 8, 14. Here AB / DE = 4/6 = 2/3 and BC/CE = 6/8 = 3/4. Therefore this is not possible.
Statement II: Sides are 8, 12, 16. Here AB / DE = BC/CE = AC/CD = 1/2. Therefore this is possible.
Statement III: Sides are 16, 24, 32. Here AB / DE = BC/CE = AC/CD = 1/4. Therefore this is possible.
Option D
Arun Kumar
30 Dec 2020, 06:49
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Both ABC and CDE triangle are similar through AAA similarity. Hence, their corresponding sides would also be equal.
Attached screen for the explanation of similarity of both triangles.
We now know all the side lengths of triangle CDE i.e. 4,6,8.
I) Won't fit in. Incorrect.
II) If 4,6,8 could be the lengths of side then 8,12,16 could also be possible sides as this is multiple of original lengths. Correct.
III) Similar to II. 16,24,32 is also possible. Correct.
Answer:- D
Attached screen for the explanation of similarity of both triangles.
We now know all the side lengths of triangle CDE i.e. 4,6,8.
I) Won't fit in. Incorrect.
II) If 4,6,8 could be the lengths of side then 8,12,16 could also be possible sides as this is multiple of original lengths. Correct.
III) Similar to II. 16,24,32 is also possible. Correct.
Answer:- D
Attachments
File comment: Similarity of both triangles.
20201230_190945.jpg [ 829.73 KiB | Viewed 3186 times ]
