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28 Mar 2023, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:58) correct
20%
(02:28)
wrong
based on 74
sessions
History
Date
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What is the length of side AB in equilateral triangle ABC if the length of altitude AD to side BC is 12?
A. 8√3
B. 10√2
C. 18
D. 12√3
E. 24
Attachment:
download.png [ 989 Bytes | Viewed 2440 times ]
28 Mar 2023, 02:58
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Bunuel
\(\frac{AD}{BC} = \frac{AD }{ AB} = 12\)
In \(\triangle ABD \)
- \(\angle ABD = 60\)
- \(\angle ADB = 90\)
- \(\angle BAD = 30\)
\(AB = \frac{2}{\sqrt{3}} * AD\)
\(AB = \frac{2}{\sqrt{3}} * 12\)
\(AB = \frac{2 \sqrt{3}}{\sqrt{3}*\sqrt{3}} * AD\)
\(AB = \frac{2\sqrt{3}}{3} * 12\)
\(AB = 8\sqrt{3}\)
Option A
30 Mar 2023, 02:46
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Hey gmatophobia thank you for your explanation! I have two questions:
How do you get the 2/√3 in the first step?
And why do multiply by √3 in the third step?
Thank you in advance!
How do you get the 2/√3 in the first step?
And why do multiply by √3 in the third step?
Thank you in advance!
