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

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

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30 Nov 2018, 10:03
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45% (medium)

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60% (01:24) correct 40% (01:21) wrong based on 111 sessions

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Project DS Butler: Day 25: Data Sufficiency (DS49)

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In the figure above, Rand 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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Joined: 10 Sep 2018
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Re: In the figure above, Rand Q are points on the x-axis. What is the area  [#permalink]

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30 Nov 2018, 10:48
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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In the figure above, Rand Q are points on the x-axis. What is the area  [#permalink]

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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.

In the figure above, Rand Q are points on the x-axis. What is the area   [#permalink] 30 Nov 2018, 20:15
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