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# A triangle PQR has angle PQR as 105 degrees. What is the area of

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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25 Jun 2018, 09:53
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2
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Difficulty:

55% (hard)

Question Stats:

52% (01:37) correct 48% (01:32) wrong based on 40 sessions

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A triangle PQR has angle PQR as 105 degrees. What is the area of triangle PQR?

(1) Length of PQ is 5 units.

(2) Angle PRQ is 30 degrees.
Intern
Joined: 19 Jun 2018
Posts: 4
Re: A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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25 Jun 2018, 10:57
We can't find the area until we know the second side. A stmt not enough. Using B alone we can find the third angle but not side measurment

To use SIN theory we need angle and side. Using both the stmt we can find the area.

C

Sent from my SM-G892U using GMAT Club Forum mobile app
Manager
Joined: 13 Feb 2018
Posts: 135
Re: A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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26 Jun 2018, 02:11
Miller116 wrote:
We can't find the area until we know the second side. A stmt not enough. Using B alone we can find the third angle but not side measurment

To use SIN theory we need angle and side. Using both the stmt we can find the area.

C

Sent from my SM-G892U using GMAT Club Forum mobile app

There should be some other explanations, GMAT doesn't test SIN knowledge IMO
Manager
Joined: 13 Feb 2018
Posts: 135
A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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26 Jun 2018, 02:27
1
When I thought a bit, here is my approach:

We have to draw height PD from P angle to QR segment. No w we have got two right triangles PDR and PDQ
Lets check triangle PQD. Angle PQD is 45 degree and angle PDQ is 90 degree, we can find angle QPD=45. This triangle is isosceles right triangle with 45 degree phenomenon, As we know PQ=5 we can calculate every side.
Now let's check triangle PDR. As we know PRD angle is 30 degree and PDR angle 90 degree, we have got right triangle with 30 degree phenomenon and as we already know PD side we can calculate every side.

Area of the triangle PQR=PD*(QD+DR)/2

In My Opinion
Ans: C

P.S Couldn't find how to attach files, to show the figure illustration. Sorry for my bad
Intern
Joined: 02 Mar 2017
Posts: 3
Re: A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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26 Jun 2018, 12:40
LevanKhukhunashvili wrote:
When I thought a bit, here is my approach:

We have to draw height PD from P angle to QR segment. No w we have got two right triangles PDR and PDQ
Lets check triangle PQD. Angle PQD is 45 degree and angle PDQ is 90 degree, we can find angle QPD=45. This triangle is isosceles right triangle with 45 degree phenomenon, As we know PQ=5 we can calculate every side.
Now let's check triangle PDR. As we know PRD angle is 30 degree and PDR angle 90 degree, we have got right triangle with 30 degree phenomenon and as we already know PD side we can calculate every side.

Area of the triangle PQR=PD*(QD+DR)/2

In My Opinion
Ans: C

P.S Couldn't find how to attach files, to show the figure illustration. Sorry for my bad

How can Angle PQD be 45?
PQD = 180-PQR => 180 - 105 => So PQD=75
Intern
Joined: 02 Mar 2017
Posts: 3
Re: A triangle PQR has angle PQR as 105 degrees. What is the area of  [#permalink]

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26 Jun 2018, 12:43
1
amanvermagmat wrote:
A triangle PQR has angle PQR as 105 degrees. What is the area of triangle PQR?

(1) Length of PQ is 5 units.

(2) Angle PRQ is 30 degrees.

Attached solution

Sent from my iPhone using GMAT Club Forum mobile app
Re: A triangle PQR has angle PQR as 105 degrees. What is the area of &nbs [#permalink] 26 Jun 2018, 12:43
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# A triangle PQR has angle PQR as 105 degrees. What is the area of

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