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If in the figure above OR = 5, what is the length of QR?

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Bunuel
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If in the figure above OR = 5, what is the length of QR? [#permalink] New post   29 Aug 2018, 02:21
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If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.


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Re: If in the figure above OR = 5, what is the length of QR? [#permalink] New post   29 Aug 2018, 02:29
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Bunuel wrote:

If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.


Show Spoiler
Attachment:
image002.jpg


(1) The measure of angle QOR = 60.
It means QOR=ROQ=OQR=60=equilateral triangle QR=5
sufficient.

(2) The area of the triangle POR is 25.
area = b*h/2
no b , no h
insufficient.

A
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Re: If in the figure above OR = 5, what is the length of QR? [#permalink] New post   29 Aug 2018, 02:32
External Angle = Sum of the two interior Angles.

Angle OPQ + Anlge POQ = Angle OQR = 60.
30 + Angle POQ = 60
Angle POQ = 30.

From statement 1:

Given Angle QOR = 60. Means Angle POR is 90.
Then Angle ORP becomes 60.
OQR becomes equilateral triangle.

Then OR = QR = 5.
Sufficient.

From 2:

No idea about other angles.
Insufficient.

A is the answer.
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Re: If in the figure above OR = 5, what is the length of QR? [#permalink] New post   29 Aug 2018, 02:38
Bunuel wrote:

If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.
Show Spoiler
Attachment:
image002.jpg


Question stem:- what is the length of QR?

St1:- The measure of angle QOR = 60.

So, OQR is an equilateral triangle with QR=QO=OR=5 (In triangle OQR, Angle Q=Angle O=60, so Angle R=180-60-60=60. All angles are equal , hence all sides are equal)
Sufficient.

St2:- The area of the triangle POR is 25.
One angle, one side and area of triangle is given. We need one more criteria to determine area.
Insufficient.

Ans. (A)
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Re: If in the figure above OR = 5, what is the length of QR? [#permalink] New post   29 Aug 2018, 02:57
Bunuel wrote:

If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.


Show Spoiler
Attachment:
image002.jpg
St1) triangle OQR is equilateral.
So each side is equal in this triangle.
Sufficient

St2) you are given area with OR as fixed length. Now the angle ORQ is not fixed. One can tilt it at a different angle.
We have

area = base * perpendicular height

Area is fixed. So we can keep changing the perpendicular height by changing the tilt of the line QR and hence base value will keep on changing to give a fixed area.

This requires a bit of imagination but that's the beauty of geometry DS questions

Answer is A



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Re: If in the figure above OR = 5, what is the length of QR? [#permalink]
29 Aug 2018, 02:57
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Bunuel
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