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# Two parallel lines L1 and L2 lie in a plane at a perpendicular distanc

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Two parallel lines L1 and L2 lie in a plane at a perpendicular distanc  [#permalink]

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28 Jun 2018, 10:12
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:49) correct 35% (01:55) wrong based on 23 sessions

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Two parallel lines L1 and L2 lie in a plane at a perpendicular distance of 5 units from each other. A triangle ABC is drawn such that points A, B lie on L1 while point C lies on L2. Similarly a parallelogram PQRS is also drawn such that points P, Q lie on L1 while points R, S lie on L2. What is the ratio of area of triangle ABC to that of parallelogram PQRS?

(1) PQ = 3 units.

(2) AB = PQ.
Intern
Joined: 03 Mar 2018
Posts: 31
GMAT 1: 620 Q44 V31
Re: Two parallel lines L1 and L2 lie in a plane at a perpendicular distanc  [#permalink]

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28 Jun 2018, 11:26
1
amanvermagmat wrote:
Two parallel lines L1 and L2 lie in a plane at a perpendicular distance of 5 units from each other. A triangle ABC is drawn such that points A, B lie on L1 while point C lies on L2. Similarly a parallelogram PQRS is also drawn such that points P, Q lie on L1 while points R, S lie on L2. What is the ratio of area of triangle ABC to that of parallelogram PQRS?

(1) PQ = 3 units.

(2) AB = PQ.

2 parallel line L1 and L2 and a distance between them is 5 units.
Area of triangle ABC = 1/2 * AB (base) * height (lets call it MN) = 5/2*AB
Area of parallelogram = MN * PQ =5*PQ

We need to find the ratio of areas of ABC and PQRS.

Statement 1: PQ = 3 units. Clearly insufficient.

Statement 2: AB = PQ

Area of ABC =5/2*AB = 2.5*(AB) and Area of PQRS = 5*PQ

Ratio of areas = Area of ABC / Area of PQRS = 2.5*AB / 5*PQ

Since AB = PQ; Ratio of areas = 2.5/5 = 1/2. Therefore, Statement 2 is Sufficient.

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Re: Two parallel lines L1 and L2 lie in a plane at a perpendicular distanc &nbs [#permalink] 28 Jun 2018, 11:26
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