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A flat triangular cornfield has the dimensions shown in the figure abo

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A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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New post Updated on: 24 Feb 2015, 14:53
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A flat triangular cornfield has the dimensions shown in the figure above. If y^2 = 2, what is the area of the field in square miles?

(A) 1/4
(B) √3/4
(C) 1/2
(D) √3/2
(E) 1

Originally posted by phangureh on 24 Dec 2009, 13:11.
Last edited by Bunuel on 24 Feb 2015, 14:53, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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New post 25 Dec 2009, 05:53
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phangureh wrote:
Image
A flat triangular cornfield has the dimensions shown in the figure above. If y^2 = 2, what is the area of the field in square miles?

(A) 1/4
(B) √3/4
(C) 1/2
(D) √3/2
(E) 1


\(Area=\frac{Base*Heigt}{2}\)

\(Hypotenuse=\sqrt{2}\)

\(Base = \frac{y}{2}=\frac{\sqrt{2}}{2}\)

\(Height=\sqrt{\sqrt{2}^2-(\frac{\sqrt2}{2})^2}=\sqrt{2-\frac{1}{2}}=\frac{\sqrt3}{\sqrt2}\) (Pythagora's)

\(Area=\frac{Base*Heigt}{2}=\frac{1}{2}*\frac{\sqrt{2}}{2}*\frac{\sqrt3}{\sqrt2}=\frac{\sqrt{3}}{4}\)
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Re: A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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New post 24 Dec 2009, 22:25
phangureh wrote:
Anyone know how to do this?

1) A flat triangular cornfield has the dimensions shown in the figure above. If y^2 = 2, what is the area of the field in square miles?

The figure is a right triangle with the hypotenuse Y miles and one of the legs is Y/2 miles

Answer is square root 3 / 4


can you please post the figure in the question.....not able to view it
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A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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New post 15 May 2017, 09:07
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phangureh wrote:
Attachment:
gmat190507-1-735112.jpg
A flat triangular cornfield has the dimensions shown in the figure above. If y^2 = 2, what is the area of the field in square miles?

(A) 1/4
(B) √3/4
(C) 1/2
(D) √3/2
(E) 1


If a right triangle's hypotenuse is twice the length of the shorter leg (here, hypotenuse = y and shorter leg = \(\frac{y}{2}\)), it is a 30-60-90 triangle with side ratio x : \(\sqrt{3}\)x : 2x

We also know that \(y^2\)=2

Take the square root of both sides to get y = \(\sqrt{2}\)

Short leg is \(\frac{y}{2}\) = \(\frac{√2}{2}\)

Longer leg is \(\sqrt{3}\)*\(\frac{√2}{2}\) = \(\frac{√6}{2}\)

Area = (b*h)/2

\(\frac{√6}{2}\) * \(\frac{√2}{2}\) divided by 2

\(\frac{√12}{4}\) = \(\frac{(2√3)}{4}\) divided by 2

\(\frac{(2√3)}{4}\) ÷ 2 = \(\frac{(2√3)}{8}\)= \(\frac{√3}{4}\)

Answer B
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Re: A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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New post 10 Apr 2019, 08:26
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A flat triangular cornfield has the dimensions shown in the figure abo   [#permalink] 10 Apr 2019, 08:26
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