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A flat triangular cornfield has the dimensions where the

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Intern
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A flat triangular cornfield has the dimensions where the [#permalink] New post 04 Oct 2006, 08:40
A flat triangular cornfield has the dimensions where the hypotenuse=y miles, the height=y/2 and the dimensions of the base are unknown. If y squared = 2, what is the area of the field in sqare miles?

A)1/4
B)ROOT 3/4
C)1/2
D)ROOT 3/2
E)1
Director
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GMAT Tests User
 [#permalink] New post 04 Oct 2006, 10:40
b2 = hypt2 - height2
b^2 = sqrt(2)^2 - (sqrt(2)/2)^2
b^2 = 2 - 1/2
b^2 = 3/2
b = sqrt(3)/sqrt(2)

1/2 * sqrt(3)/sqrt(2) * sqrt(2)/2
= sqrt(3)/4 Answer
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 [#permalink] New post 04 Oct 2006, 12:48
Answer B. Side opposite to 30degree is always helf of the hyp.Since height is y/2 hence angle with the base is 30degree.The base is hence root(3) /2 y..Hence area is SQRT 3 /4
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 [#permalink] New post 04 Oct 2006, 13:54
B
(Y/2)^2 + X^2 = Y^2

Since, Y^2 = 2, substitute and simplify:

X = sqrt(3/2)

Area = 1/2*sqrt(3/2)*sqrt(1/2)

= sqrt3/4
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 [#permalink] New post 04 Oct 2006, 14:16
base = 2 - (y/2)^2
area = (sqrt(1.5)/2) x (sqrt(2)/2) = sqrt 3/4
  [#permalink] 04 Oct 2006, 14:16
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