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# In the figure shown, the square ABCD is inscribed in the triangle EFG.

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GMATH Teacher
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Joined: 12 Oct 2010
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In the figure shown, the square ABCD is inscribed in the triangle EFG.  [#permalink]

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04 Feb 2019, 12:44
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Difficulty:

75% (hard)

Question Stats:

42% (02:01) correct 58% (01:29) wrong based on 38 sessions

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GMATH practice question (Quant Class 17)

In the figure shown, the square ABCD is inscribed in the triangle EFG. What is the perimeter of the square?

(1) FG = 10
(2) The distance from E to the line FG is 6.

Source: https://gmath.net

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04-Feb19-9h.gif [ 3.55 KiB | Viewed 484 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: In the figure shown, the square ABCD is inscribed in the triangle EFG.  [#permalink]

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04 Feb 2019, 21:55
Hi fskilnik,

Even I like many others had marked option E, could you please explain how both statements together are sufficient to find the perimeter of the square?
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Re: In the figure shown, the square ABCD is inscribed in the triangle EFG.  [#permalink]

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05 Feb 2019, 05:59
DarkHorse2019 wrote:
Hi fskilnik,

Even I like many others had marked option E, could you please explain how both statements together are sufficient to find the perimeter of the square?

Hi, DarkHorse2019 !

Thank you for your interest in my question/solution and sorry for the small delay in coming back here.

My solution will be posted below in a few minutes.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: In the figure shown, the square ABCD is inscribed in the triangle EFG.  [#permalink]

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05 Feb 2019, 06:11
1
fskilnik wrote:

GMATH practice question (Quant Class 17)

In the figure shown, the square ABCD is inscribed in the triangle EFG. What is the perimeter of the square?

(1) FG = 10
(2) The distance from E to the line FG is 6.

Source: https://gmath.net

$$? = 4x\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = x\,}$$

Each statement alone is not sufficient, as proved by the geometric bifurcations presented in the figure above.

$$\left( {1 + 2} \right)\,\,\,\Delta EAB\,\, \cong \,\,\Delta EGF\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{{6 - x} \over 6} = {{AB} \over {GF}} = {x \over {10}}$$

$$10\left( {6 - x} \right) = 6x\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,\,{\rm{unique}}$$

The correct answer is therefore (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: In the figure shown, the square ABCD is inscribed in the triangle EFG.   [#permalink] 05 Feb 2019, 06:11
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# In the figure shown, the square ABCD is inscribed in the triangle EFG.

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