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# If OP is parallel to RQ, What is the ratio of the perimeter of OPS to

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
If OP is parallel to RQ, What is the ratio of the perimeter of OPS to  [#permalink]

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11 Sep 2018, 23:41
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:26) correct 31% (00:37) wrong based on 15 sessions

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If OP is parallel to RQ, What is the ratio of the perimeter of OPS to that of RQS?

(1) The ratio of the length of PQ to the length of QS is 2 : 1.
(2) The ratio of the length of OP to the length of RQ is 3 : 1.

Attachment:

image001 (1).jpg [ 2.59 KiB | Viewed 360 times ]

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Re: If OP is parallel to RQ, What is the ratio of the perimeter of OPS to  [#permalink]

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12 Sep 2018, 07:25
Bunuel wrote:

If OP is parallel to RQ, What is the ratio of the perimeter of OPS to that of RQS?

(1) The ratio of the length of PQ to the length of QS is 2 : 1.
(2) The ratio of the length of OP to the length of RQ is 3 : 1.

Attachment:
image001 (1).jpg

Question: What is the ratio of perimeter of OPS to RQS ?

Since two sides 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. $$A_1/A_2 = (S_1/S_2)^2$$
and ratio fo perimeters of two triangles, $$P_1/P_2 = (S_1/S_2)$$
Therefore need only the ratio of sides of two similar triangles in this case

Statement 1: The ratio of the length of PQ to the length of QS is 2 : 1.
i.e. $$(S_1/S_2) = 3/1$$
SUFFICIENT

Statement 2: The ratio of the length of OP to the length of RQ is 3 : 1

i.e. $$(S_1/S_2) = 3/1$$
SUFFICIENT

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Re: If OP is parallel to RQ, What is the ratio of the perimeter of OPS to &nbs [#permalink] 12 Sep 2018, 07:25
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