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Isosceles to equilateral

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by bhumika.k.shah » Sat Feb 27, 2010 2:31 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. sqrt 2/ 2
B. sqrt 3/ 2
C. sqrt3/ sqrt2* (2)
D. sqrt 2 / sqrt 3
E. 3/2

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though i got this question correct. i took a lot of time . in the OE , they have said one way to look at this sum. which is the exact same method ive done. But i donot know any other different, quicker approach.
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by sanju09 » Sat Feb 27, 2010 2:48 am
bhumika.k.shah wrote: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. sqrt 2/ 2
B. sqrt 3/ 2
C. sqrt3/ sqrt2* (2)
D. sqrt 2 / sqrt 3
E. 3/2

Source MGMAT QB

though i got this question correct. i took a lot of time . in the OE , they have said one way to look at this sum. which is the exact same method ive done. But i donot know any other different, quicker approach.
Let AC = h, is the hypotenuse of isosceles right triangle ABC, so that h could be the height of equilateral triangle DEF.

Now, AB = BC = h/√2 and DE = EF = FD = 2 h/√3, such that any

AB:DE = h/√2: 2 h/√3 = [spoiler]√3:2 √2[/spoiler].

[spoiler]C[/spoiler]
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