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angle of a rhombus is 60°

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by sanju09 » Thu Sep 15, 2011 4:10 am
If the measure of one angle of a rhombus is 60°, then the ratio of the length of its longer diagonal to the length of its shorter diagonal is
(A) 2
(B) √3
(C) √2
(D) √3/2
(E) √2/2


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by cans » Thu Sep 15, 2011 4:16 am
Diagonals of rhombus bisect at 90 degree. Thus tan 30 = shorter/longer,
or longer/shorter = 1/tan 30 = √3
IMO B
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by sanju09 » Thu Sep 15, 2011 4:26 am
cans wrote:Diagonals of rhombus bisect at 90 degree. Thus tan 30 = shorter/longer,
or longer/shorter = 1/tan 30 = √3
IMO B
Use of trigonometric ratios is not general on GMAT. It's better if we explain it by using 30-60-90 triangle's concept or by any other geometric concept.
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by sam2304 » Thu Sep 15, 2011 4:49 am
Image

Diagonals bisect @ 90 degree. So the smaller triangle is 30 60 90 -> 2 1 rt3.
Ratio of longer/shorter = rt3(2)/2 = rt3

IMO B.
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by sanju09 » Thu Sep 15, 2011 4:54 am
sam2304 wrote:Image

Diagonals bisect @ 90 degree. So the smaller triangle is 30 60 90 -> 2 1 rt3.
Ratio of longer/shorter = rt3(2)/2 = rt3

IMO B.
OA is [spoiler]B[/spoiler]
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