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AB is parallel to CD.

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AB is parallel to CD. [#permalink] New post 22 May 2017, 01:47
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Question Stats:

53% (01:24) correct 46% (00:59) wrong based on 26 sessions


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AB is parallel to CD.
AD is parallel to BC.
2AD = EG

Quantity A
Quantity B
The area of ABCD
The area of EFG



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: AB is parallel to CD. [#permalink] New post 22 May 2017, 07:20
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Expert's post
Carcass wrote:


Image

AB is parallel to CD.
AD is parallel to BC.
2AD = EG

Quantity A
Quantity B
The area of ABCD
The area of EFG




The given information tells us that ABCD is a parallelogram, which means the area = (base)(height)
Let x = the length of the base (AD)
We're told that L = the height of the parallelogram
So, the area of ABCD = (x)(L)

Area of triangle = (base)(height)/2
Given: 2AD = EG
We already let x = the length of AD
So, EG = 2x
In other words, the length of the triangle's base = 2x
We're told that L = the height of the triangle
So, the area of triangle EFG = (L)(2x)/2 = (L)(x)

We have:
Quantity A: (x)(L)
Quantity B: (L)(x)

Answer:
[Reveal] Spoiler:
C


Cheers,
Brent
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Re: AB is parallel to CD. [#permalink] New post 29 Sep 2018, 11:47
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Re: AB is parallel to CD.   [#permalink] 29 Sep 2018, 11:47
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