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In the figure above, Rand Q are points on the x-axis. What is the area

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GMATBusters
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In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  30 Nov 2018, 10:03
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In the figure above, R and Q are points on the x-axis. What is the area of equilateral triangle PQR ?

(1) The coordinates of point Pare (6, 2 \(\sqrt{3}\)) .
(2) The coordinates of point Q are (8, 0).
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NCRanjan
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  30 Nov 2018, 10:48
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Answer is A alone is sufficient
Drop a median ( PS) from P to X axis . since it is an equilateral triangle the median will be at 90 degrees on X axis and will be an angle bisector at P . Now this triangle PSR or PSQ are 30-60-90 triangles since we know PS - it is 2root3 we can find out QS and hence the base of the triangle . so we can find the area out

Coming to option B . well the equilaterla triange can have any base , it can be 8 , or 6 or 4 , or 7 and we have no clue about the height so it is not sufficient

A seems to be the answer
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  30 Nov 2018, 20:15
1) The coordinates of point P (6, 2 √3) .

as we know the height of the equilateral triangle: 2 √3, we can calculate the hypotenuse (PR), which enable to calculate the area of the equilateral triangle (4/√3 x (PR)^2). Sufficient

2)The coordinates of point Q are (8, 0)

Not able to calculate any of its length of the triangle. Not sufficient.

IMO: A is the answer
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  29 Sep 2019, 15:44
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This might help some people.

Statement (1) is sufficient as we are given the height and we already know it is an equilateral triangle.

Statement (2) is insufficient as we don't know the gap between the origin and the first point
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Soumya92
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  14 Dec 2020, 06:30
IMO may also be C.

Because, RQ= 4 & PS= 2√3

Posted from my mobile device
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Rainman91
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  27 Jul 2022, 21:20
I did it this way. Height of equilateral triangle (h) = (A√3)/2. (A is the side of an triangle)

Plug 2sqrt/3 into H, we can solve for A.

We got the Base. We have both BxH divide by 2.
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink] New post  01 Jul 2023, 18:45
GMATBusters wrote:
In the figure above, R and Q are points on the x-axis. What is the area of equilateral triangle PQR ?

(1) The coordinates of point P are (6, 2 \(\sqrt{3}\))

Drop a median from P.
Now it become 30-60-90 Triangle and one side opposite to 60 degrees angle is known.
\(1:\sqrt{3}:2\)

Hence, sufficient

(2) The coordinates of point Q are (8, 0)

Definitely not sufficient.

Hence, Option (A)
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Re: In the figure above, Rand Q are points on the x-axis. What is the area [#permalink]
01 Jul 2023, 18:45
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