fskilnik@GMATH wrote:
<b>GMATH</b> 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.
$$\left( {1 + 2} \right)\,\,\,\Delta EAB\,\, \cong \,\,\Delta EGF\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{6 - x}}{6} = \frac{{AB}}{{GF}} = \frac{x}{{10}}$$
$$10\left( {6 - x} \right) = 6x\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,\,{\text{unique}}$$
The correct answer is therefore (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
