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# What is the area of triangle PQR? (1) angle PQR is 120 degrees

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What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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16 Mar 2018, 07:12
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45% (medium)

Question Stats:

63% (01:12) correct 37% (01:20) wrong based on 83 sessions

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What is the area of triangle PQR?

(1) angle PQR is 120 degrees

(2) PQ=5 units and PR=10 units
Intern
Joined: 25 Jan 2018
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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16 Mar 2018, 07:38
area of triangle ab sin(theta) , where a and b are the sides of the triangle and theta is the angle between them. so my answer is 25
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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18 Mar 2018, 11:23
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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18 Mar 2018, 12:57
1
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle

Ans:C
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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19 Mar 2018, 10:15
Quote:
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle

Hi Leo8,

Awesome explanation.

Just wanna add that SSA gives 2 solutions using the law of sines. I'm not sure if we can use the law of sines given that PQR is obtuse?
https://www.mathsisfun.com/algebra/trig ... ngles.html
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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20 Mar 2018, 06:55
1
Hi

Please see this similar question: https://gmatclub.com/forum/what-is-the- ... l#p2027164

This Question is based on a very IMPORTANT EXCEPTION:

The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS, or
Angle-Side-Side) does not always prove congruence, even when the equal angles are opposite equal sides.

Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the
known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In
all other cases with corresponding equalities, SSA proves congruence.

The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known
as the HL (Hypotenuse-Leg) condition or the RHS (Right-angle-Hypotenuse-Side) condition), we can calculate the
third side and fall back on SSS.

If any triangle follows laws of Congruency, it means it can be drawn Uniquely. Hence sufficient.

Akela wrote:
Quote:
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle

Hi Leo8,

Awesome explanation.

Just wanna add that SSA gives 2 solutions using the law of sines. I'm not sure if we can use the law of sines given that PQR is obtuse?
https://www.mathsisfun.com/algebra/trig ... ngles.html

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WhatsApp Image 2018-03-09 at 21.13.07 %281%29.jpeg [ 109.55 KiB | Viewed 1351 times ]

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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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22 Mar 2018, 23:35
Akela wrote:
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient

Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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23 Mar 2018, 00:11
Hi
First remember if you can draw a triangle or any figure uniquely, you can find any parameter related to the figure, it's area, perimeter, any angle, side, diagonal etc.

Now remember, if any triangle satisfy the law of congruency, it can be drawn uniquely.

In this question , we have proved that it is a unique triangle drawn as per given conditions. Hence area can be found out.

Let me know what u haven't understood?

Tanvi94 wrote:
Akela wrote:
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient

Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below

Posted from my mobile device
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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

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23 Mar 2018, 08:22
Quote:
Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below

Hi!

So, st. 1 itself is not sufficient.

St. 2 PQ =5, PR =10 => we can make infinite number of triangles (see attached pic)

St 1 + st 2. If angle PQR = 120, PQ=5, PR=10, we can draw only one triangle. Not sure? Try to draw another type
Therefore, we can find the area of the triangle. Please note that in DS questions we do not have to find the value of the area like in PS. We just have to know whether we CAN find the area with the data provided. So, as we can draw only ONE triangle with given values we will be able to calculate the area.

Hope this helps!
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Untitled.png [ 14.51 KiB | Viewed 1222 times ]

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Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees   [#permalink] 23 Mar 2018, 08:22
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