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

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
In the figure above, square ABCE has an area of 81, and points G and F  [#permalink]

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26 Nov 2019, 01:59
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40% (01:31) correct 60% (01:26) wrong based on 5 sessions

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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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Trapezoid2.jpg [ 15.8 KiB | Viewed 183 times ]
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Joined: 19 Oct 2018
Posts: 1151
Location: India
Re: In the figure above, square ABCE has an area of 81, and points G and F  [#permalink]

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

GF= 1/3*9=3

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:

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
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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