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Mastering Important Concept on Triangles – III - Question #1

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EgmatQuantExpert
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Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   Updated on: 15 Dec 2016, 23:50
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Mastering Important Concept on Triangles – III - Question #1


In the given figure, BD is the median of triangle ABC and the lines BD and CE intersect at point F. If the area of triangle BFC is \(6cm^2\) and area of the quadrilateral FEAD is \(18cm^2\). Find the area of triangle FDC, if the ratio of the area of triangle FDC and triangle FEB is \(3:2\).




Answer Choices

    a. \(12 cm^2\)
    b. \(18 cm^2\)
    c. \(24 cm^2\)
    d. \(36 cm^2\)
    e. \(42 cm^2\)





Key concepts on Triangles are explained in detail in the following posts:

1. Mastering Important Concepts Tested By GMAT in Triangle - I

2. Mastering Important Concepts Tested By GMAT in Triangle - II

3.Mastering Important Concepts Tested By GMAT in Triangle - III


Detailed solution will be posted soon. :)

Thanks,
Saquib
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e-GMAT

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Official Answer
D

Originally posted by EgmatQuantExpert on 11 Dec 2016, 08:29.
Last edited by EgmatQuantExpert on 15 Dec 2016, 23:50, edited 1 time in total.
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Re: Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   Updated on: 15 Dec 2016, 23:49
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Hey,

PFB the official solution :)

It is given that BD is the median of the triangle ABC.

From the given information we can conclude that:
    • Area of Triangle ABD = Area of Triangle BDC
Which is equal to,
    • Area of Triangle FEB + Area of Quadrilateral FEAD = Area of Triangle BFC + Area of Triangle FDC…. (i)

We are also given the following information –
    • Area of BFC = \(6 cm^2\)
    • Area of Quadrilateral FEAD = \(18cm^2\)
    • And area of FDC: Area of FEB = 3: 2
      o Let us consider the area of FDC and FEB to be \(3x\) and \(2x\) respectively.

Let us substitute the above values in equation (i)
    • Area of Triangle FEB + Area of Quadrilateral FEAD = Area of Triangle BFC + Area of Triangle FDC
      o \(2x + 18 = 6 + 3x\)
      o \(x = 12 cm^2\)
      • Thus the Area of Triangle FDC = \(3x = 36 cm^2\)

Hence the correct answer option is D


Thanks,
Saquib
Quant Expert
e-GMAT

Originally posted by EgmatQuantExpert on 11 Dec 2016, 08:31.
Last edited by EgmatQuantExpert on 15 Dec 2016, 23:49, edited 1 time in total.
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Re: Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   14 Dec 2016, 22:14
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Since BD is median , The area of triangle BDA= Area of triangle BDC

The area of triangle BDA= Area of triangle BDC

Area of BFE+ Area EFAD = Area BFC+ Area CFD

2x + 18 = 3x+ 6

X= 12.

we need 3x = 36 cm^2
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Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   15 Dec 2016, 23:54
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Hey Everyone,

The official solution has been posted. Please go through the solution once. In case of any doubts please feel to ask :) :)

Thanks,
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Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   31 Aug 2017, 14:31
As BD is the median , it divides triangle ABC into two triangles of equal area.

Area of triangle ABD = Area of triangle BDC
Area of triangle BFE + Area of quadilateral EAFD = Area of triangle BFC + Area of triangle FDC ........(1)

Also, Area of FDC/Area of FEB = 3/2
which gives us , Area of FEB = 2*Area of FDC / 3

Substituting above relation in our equation (1)

2*Area of FDC / 3 +Area of EFAD = Area of BFC + Area of FDC
Area of FDC/3 = Area of EFAD - Area of BFC
Area of FDC = 3( 18-6)
Area of FDC = 36 cm^2

Option D
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Mastering Important Concept on Triangles – III - Question #1 [#permalink] New post   18 Sep 2019, 08:46
Quote:

In the given figure, BD is the median of triangle ABC and the lines BD and CE intersect at point F. If the area of triangle BFC is \(6cm^2\) and area of the quadrilateral FEAD is \(18cm^2\). Find the area of triangle FDC, if the ratio of the area of triangle FDC and triangle FEB is \(3:2\).




Answer Choices

    a. \(12 cm^2\)
    b. \(18 cm^2\)
    c. \(24 cm^2\)
    d. \(36 cm^2\)
    e. \(42 cm^2\)



Since we are not given much of the data we should try to use that is given. We are told that BD is the median which means it divides the area into half.
That means the two sides of the median should be equal to each other.
Now out of 4 portions total, we are given area in numerical values for 2 of them and for the other 2, we are given ratios.
So we can form the equation :
\(2x+18=6+3x\)
\(x=12\)
But we are not asked what is \(x\). (Trust me, I was going to mark A)
We are asked
\(Area of Triangle FDC = 3x=36cm2\)
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Re: Mastering Important Concept on Triangles III - Question #1 [#permalink] New post   18 Aug 2023, 13:22
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Re: Mastering Important Concept on Triangles III - Question #1 [#permalink]
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