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ratio of a leg

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by sanju09 » Fri May 07, 2010 5:24 am
If the hypotenuse of isosceles right triangle ABC has the same length as the height of equilateral triangle DEF, what is the ratio of a leg of triangle ABC to a side of triangle DEF?
(A) √2/√3
(B) √3/ (2 √2)
(C) √2/2
(D) √3/2
(E) 3/√2
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by pradeepkaushal9518 » Fri May 07, 2010 5:33 am
ans is B

taking a as a side and a root 2 as the hypotenuse equal to height of equilateral triangle

ratio of height to side is a root 3 : 2a
hence for side a root 2 it will be 2root2/root 3

hence ratio of a to a 2 root 2/root 3 will be root 3/2 root 2
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by sanju09 » Fri May 07, 2010 5:39 am
pradeepkaushal9518 wrote:ans is B
explanation is must for IMO senders
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by pradeepkaushal9518 » Fri May 07, 2010 6:00 am
i have given the explanation. but in very short cut to reduce time.
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