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In the figure shown, the square ABCD is inscribed in the tri

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by fskilnik@GMATH » Mon Feb 04, 2019 11:37 am

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<b>GMATH</b> &nbsp;practice question &nbsp;(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.

Answer: [spoiler]____(C)__[/spoiler]

Source: https://gmath.net
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Source: — Data Sufficiency |
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by fskilnik@GMATH » Tue Feb 05, 2019 5:05 am
fskilnik@GMATH wrote:Image

<b>GMATH</b> &nbsp;practice question &nbsp;(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
Image

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

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

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

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)
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