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Geometry - Triangle

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by rijul007 » Sun Nov 06, 2011 1:52 pm
Option B

Apply Pythagoras Theorem [H^2 = B^2 + P^2]
Last edited by rijul007 on Mon Nov 07, 2011 11:23 am, edited 1 time in total.
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by neelgandham » Sun Nov 06, 2011 6:04 pm
We know the value of y(Square Root(2)) from the question. Let the angle between the side(L), which is parallel to the surface of the laptop keypad when the screen is exactly perpendicular to the keypad, and the hypotenuse be X, then

Sin X = (1/(Square Root(2)))/(Square Root(2)) = 1/2. So, from the result, we know that X = 30 degrees.

If X = 30 Degrees, Tan X = 1/(Square Root(3)) = (1/(Square Root(2)))/L, i.e. L = (Square Root(3))/(Square Root(2)).

The Area of the triangle = 0.5*L*Other side = 0.5 * [(Square Root(3))/(Square Root(2))]*(1/(Square Root(2))) = (Square Root(3))/4

Answer :B
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by shankar.ashwin » Sun Nov 06, 2011 7:31 pm
Let the base be 'B", now

B^2 + (y/2)^2 = y^2

B^2 = 3Y^2/4

B = Sqrt(3) * y / 2

Area = 1/2 bh = 1/2 * Sqrt(3) * y / 2 * y/2 = Sqrt(3) * y^2 / 8

= Sqrt(3) * 2/8 = Sqrt(3)/4 B IMO
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by Anurag@Gurome » Sun Nov 06, 2011 8:24 pm
gmatblood wrote:Please help
Let the base = x
By Pythagoras Theorem, we get y² = (y/2)² + x²
y² = (y²/4) + x²
(3/4)y² = x²
x = y√3/2
Then area of the triangular field in sq miles = (1/2) * y√3/2 * (y/2) = y²√3/8
Since y² = 2 is given in the question, so area = 2√3/8 = [spoiler]√3/4[/spoiler]

The correct answer is B.
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by thestartupguy » Mon Nov 07, 2011 5:18 am
Ans: B
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by MBA.Aspirant » Mon Nov 07, 2011 4:23 pm
√3/4
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