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In the triangle above if OP is parallel to QR, what is the ratio of NP

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In the triangle above if OP is parallel to QR, what is the ratio of NP  [#permalink]

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11 Sep 2018, 02:05
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Difficulty:

75% (hard)

Question Stats:

38% (02:17) correct 62% (01:56) wrong based on 13 sessions

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In the triangle above if OP is parallel to QR, what is the ratio of NP to PR?

(1) NR = 10
(2) The area of ONP is half of the area of QNR.

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image007.gif [ 1.56 KiB | Viewed 311 times ]

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In the triangle above if OP is parallel to QR, what is the ratio of NP  [#permalink]

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11 Sep 2018, 03:46
Bunuel wrote:

In the triangle above if OP is parallel to QR, what is the ratio of NP to PR?

(1) NR = 10
(2) The area of ONP is half of the area of QNR.

Attachment:
image007.gif

Question: what is the ratio of NP to PR?

The triangles ONP and QNR are similar triangles as the angles are same

Ratio of all corresponding sides are equal in similar triangles and also,

ratio of area of two similar triangles = square of ratio of their corresponding sides
i.e. $$A_1 / A_2 = (S_1 / S_2)^2$$

i.e. we need either ratio of corresponding sides or the ratio of area of the triangles

Statement 1: NR = 10

One side of one triangle is doesn't provide us any informatio of the other triangle hence

NOT SUFFICIENT

Statement 2: The area of ONP is half of the area of QNR.

i.e. $$A_1 / A_2 = (S_1 / S_2)^2 = 1/2$$
i.e. $$(S_1 / S_2) = 1/√2$$
i.e. $$NP/PR = S_1 / (S_2 -S_1) = 1/(√2-1)$$

SUFFICIENT

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In the triangle above if OP is parallel to QR, what is the ratio of NP &nbs [#permalink] 11 Sep 2018, 03:46
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