The equations x – y = 4 and x² + 4xy + y² = 0 represent the sides of

Acute angle between the lines x² + 4xy+ y² = 0 is $\mathrm{\pi }/3$  
The angle bisectors of ${\mathrm{x}}^2+4\mathrm{xy}+{\mathrm{y}}^2=0\text{ are }\mathrm{x}=\pm \mathrm{y}$
As x + y = 0 is perpendicular to x –y = 4, the given
triangle is isosceles with vertical angle equal to $\mathrm{\pi }/3$.
Hence, it is an equilateral triangle.