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In the figure above, square ABCE has an area of 81, and points G and F

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In the figure above, square ABCE has an area of 81, and points G and F  [#permalink]

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New post 26 Nov 2019, 01:59
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In the figure above, square ABCE has an area of 81, and points G and F trisect AB. If the area of \(\triangle{FGD}\) is 24, what is the length of HE ?

A. 3

B. \(\frac{42}{16}\)

C. 4

D. \(\frac{14}{3}\)

E. \(\frac{31}{7}\)


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Re: In the figure above, square ABCE has an area of 81, and points G and F  [#permalink]

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New post 26 Nov 2019, 02:39
square ABCE has an area of 81; hence AB=BC=CE=AE=9

GF= 1/3*9=3

Area(FGD)= 1/2*GF*AD=24

AD= \(\frac{24*2}{3}=16\)

DE=16-9=7

DHE is similar to DGA

\(\frac{HE}{GA}=\frac{DE}{AD}\)

HE=\(\frac{7*6}{16}=\frac{42}{16}\)


Bunuel wrote:
Image
In the figure above, square ABCE has an area of 81, and points G and F trisect AB. If the area of \(\triangle{FGD}\) is 24, what is the length of HE ?

A. 3

B. \(\frac{42}{16}\)

C. 4

D. \(\frac{14}{3}\)

E. \(\frac{31}{7}\)


Are You Up For the Challenge: 700 Level Questions


Attachment:
Trapezoid2.jpg
GMAT Club Bot
Re: In the figure above, square ABCE has an area of 81, and points G and F   [#permalink] 26 Nov 2019, 02:39
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In the figure above, square ABCE has an area of 81, and points G and F

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