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Intern  Joined: 11 Dec 2009
Posts: 4
A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (01:52) correct 37% (01:52) wrong based on 179 sessions

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Attachment: gmat190507-1-735112.jpg [ 9.55 KiB | Viewed 4888 times ]
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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58454
A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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phangureh wrote: 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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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
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3557
A flat triangular cornfield has the dimensions shown in the figure abo  [#permalink]

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

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

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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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