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30 Nov 2018, 10:03
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A
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Difficulty:
35%
(medium)
Question Stats:
66% (01:28) correct
34%
(01:30)
wrong
based on 986
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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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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
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
General Discussion
30 Nov 2018, 20:15
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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
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
