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


Are You Up For the Challenge: 700 Level Questions


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Trapezoid2.jpg
Trapezoid2.jpg [ 15.8 KiB | Viewed 422 times ]

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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
2
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
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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 16 Dec 2019, 12:24
nick1816 wrote:
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


Hi,

Can you please explain why did you use AD instead of FD?

Thanks
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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 16 Dec 2019, 13:27
Hello Krish728 !
The height of triangle GFD here is AD not FD, the height is always perpendicular to the base. Triangle GFD and FAD both have the same height (AD) for example.

Krish728 wrote:
nick1816 wrote:
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


Hi,

Can you please explain why did you use AD instead of FD?

Thanks

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Re: In the figure above, square ABCE has an area of 81, and points G and F   [#permalink] 16 Dec 2019, 13:27
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In the figure above, square ABCE has an area of 81, and points G and F

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