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# If Q is the midpoint of PR, what is the area of the triangle OPR?

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If Q is the midpoint of PR, what is the area of the triangle OPR?  [#permalink]

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17 Sep 2018, 22:12
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If Q is the midpoint of PR, what is the area of the triangle OPR?

(1) QR = 6.
(2) Area of OPQ is 8.

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image006.jpg [ 4.72 KiB | Viewed 527 times ]

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Re: If Q is the midpoint of PR, what is the area of the triangle OPR?  [#permalink]

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17 Sep 2018, 22:16
Since height of the two smaller triangles is the same, and we have the height, we can calculate the area of the two smaller triangles.
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Re: If Q is the midpoint of PR, what is the area of the triangle OPR?  [#permalink]

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17 Sep 2018, 22:19
option C ; straight
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Re: If Q is the midpoint of PR, what is the area of the triangle OPR?  [#permalink]

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18 Sep 2018, 20:49
Since Q divides the base equally, the area of both triangles will be the same. Hence if we are given the area of one triangle, we can calculate the are of the other one.

Statement 2 gives the area of OPQ=8. Therefore, OQR=8. Area of triangle POR= 8+8=16. Therefore sufficient, option B is the correct answer.

Please correct me if my reasoning is wrong.
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Re: If Q is the midpoint of PR, what is the area of the triangle OPR?  [#permalink]

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18 Sep 2018, 21:06
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Bunuel wrote:

If Q is the midpoint of PR, what is the area of the triangle OPR?

(1) QR = 6.
(2) Area of OPQ is 8.

Attachment:
image006.jpg

Given Q is the midpoint of PR or OQ is the median of the triangle OPR(PQ=QR)
NOTE:- Median divides the triangle symmetrically or area of triangle OPR and OQR are equal. (Area of triangle OPR=1/2*PQ*h=1/2*QR*h=Area of triangle OPR)
It's st2 , which provides area of the symmetrical triangles.
Therefore , sufficient to determine the area of OPR.

Ans. (B)
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Re: If Q is the midpoint of PR, what is the area of the triangle OPR?   [#permalink] 18 Sep 2018, 21:06
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