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niteshwaghray
GMAT 1: 700 Q45 V40
Posts: 59
Updated on: 23 May 2017, 13:18
Originally posted by niteshwaghray on 23 May 2017, 13:04.
Last edited by Bunuel on 23 May 2017, 13:18, edited 2 times in total.
Last edited by Bunuel on 23 May 2017, 13:18, edited 2 times in total.
Edited the question.
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B
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Difficulty:
45%
(medium)
Question Stats:
68% (02:08) correct
32%
(02:42)
wrong
based on 57
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In the figure below, ΔABC and ΔBCD are right-angled at points B and C respectively. If AC = \(3\sqrt{2}\), ∠ACB = \(45^∘\) and ∠CBD = \(30^∘\), what is the area of ΔBCD?
A. \(\frac{9}{4}\)
B. \(\frac{3}{2}\sqrt{3}\)
C. \(\frac{27}{4}\)
D. \(\frac{9}{2}\sqrt{3}\)
E. 9
QS430.png [ 23.52 KiB | Viewed 2895 times ]
A. \(\frac{9}{4}\)
B. \(\frac{3}{2}\sqrt{3}\)
C. \(\frac{27}{4}\)
D. \(\frac{9}{2}\sqrt{3}\)
E. 9
Attachment:
QS430.png [ 23.52 KiB | Viewed 2895 times ]
23 May 2017, 13:35
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niteshwaghray
∠ACB = 45° implies that ACB is 45°-45°-90° triangle. The sides are always in the ratio 1:1:√2. With the √2 being the hypotenuse (longest side).
Since, \(AC = 3\sqrt{2}\), then AB = BC = 3.
Next, ∠CBD = 30° implies that CBD is 30°-60°-90°. The sides are always in the ratio 1:√3:2. Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).
Since BC = 3, then CD (the smallest side opposite the smallest angle of 30°) is √3.
Finally, the area of BCD is BC*CD/2 = 3*√3/2.
Answer: B.
05 Apr 2025, 02:06
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