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# If P is the midpoint of NR, and lines OP and QR are parallel, what is

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If P is the midpoint of NR, and lines OP and QR are parallel, what is  [#permalink]

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12 Sep 2018, 00:42
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Difficulty:

55% (hard)

Question Stats:

43% (01:21) correct 57% (01:30) wrong based on 28 sessions

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If P is the midpoint of NR, and lines OP and QR are parallel, what is the area of NQR?

(1) NOP has an area of 20.
(2) QR = 7

Attachment:

image038.gif [ 1.3 KiB | Viewed 339 times ]

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If P is the midpoint of NR, and lines OP and QR are parallel, what is  [#permalink]

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12 Sep 2018, 08:16
Bunuel wrote:

If P is the midpoint of NR, and lines OP and QR are parallel, what is the area of NQR?

(1) NOP has an area of 20.
(2) QR = 7

Attachment:
image038.gif

Question: what is the area of NQR?

Since the bases of triangles are parallel therefore two triangles are similar
Ratio fo Area of two similar triangles = Square of ratio of their corresponding sides
i.e. $$A_1/A_2 = (S_1/S_2)^2$$
Also we know that $$(S_1/S_2) = 1/2$$ because P is midpoint of NR
i.e. we only need the area of small triangle to find area of big triangle in this case

Statement 1: NOP has an area of 20

SUFFICIENT

Statement 2: QR = 7

Area can't be calculated with one side hence

NOT SUFFICIENT

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Re: If P is the midpoint of NR, and lines OP and QR are parallel, what is  [#permalink]

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12 Sep 2018, 08:37

Midpoint theorem

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Since we know the height and base reduced to half their previous value, we can determine the area using answer choice (A) alone.

For further reading, here is the Source.

Bunuel wrote:

If P is the midpoint of NR, and lines OP and QR are parallel, what is the area of NQR?

(1) NOP has an area of 20.
(2) QR = 7

Attachment:
image038.gif

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Re: If P is the midpoint of NR, and lines OP and QR are parallel, what is   [#permalink] 12 Sep 2018, 08:37
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