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ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB

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ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 25 Oct 2014, 04:21
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ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB. What is the ratio of the area of triangle EFP to that of CDP?

A) 1:3
B) 1:4
C) 1:10
D) 1:9
E) 3:4

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Parallogram.png
Parallogram.png [ 7.15 KiB | Viewed 1880 times ]

Manager
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 25 Oct 2014, 04:35
Area(EFP)/Area(CFD) = (ratio of sides)^2 = (1/3)^2 = 1/9

Ans. D
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 26 Oct 2014, 10:48
itzmyzone911 wrote:
Area(EFP)/Area(CFD) = (ratio of sides)^2 = (1/3)^2 = 1/9

Ans. D



Hi,

could you please explain this formula? What about the height?

Kind regards.
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 26 Oct 2014, 11:24
LaxAvenger wrote:
itzmyzone911 wrote:
Area(EFP)/Area(CFD) = (ratio of sides)^2 = (1/3)^2 = 1/9

Ans. D



Hi,

could you please explain this formula? What about the height?

Kind regards.


This formula takes care of the height.

Ratio of areas of two similar triangles (triangle 1 and triangle 2) = (0.5*base1*height1)/(0.5*base2*height2) = (base1/base2)*(height1/height2)

Remember, in similar triangles ratio of any CORRESPONDING dimensions of the two triangles is constant. This means ratio of corresponding sides = ratio of corresponding heights = ratio of corresponding medians = ratio of corresponding angle bisectors etc. etc. = 1/3

Hence, reqd. ratio = (1/3)*(1/3) = 1/9
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 28 Oct 2014, 03:31
Refer diagram below:
Attachment:
Parallogram.png
Parallogram.png [ 4.6 KiB | Viewed 1599 times ]


Alternate angles are congruent; opposite angles are congruent

DC = 3 times EF

So, height of \(\triangle\) CDP = 3 times height of \(\triangle\) EFP

\(\frac{Area \triangle CDP}{Area \triangle EFP} = \frac{1}{3} * \frac{1}{3} = \frac{1}{9}\)

Answer = D
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB [#permalink]

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New post 04 Feb 2018, 16:15
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Re: ABCD is a parallelogram. E and F are points on AB such that AE=EF=FB   [#permalink] 04 Feb 2018, 16:15
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