A triangular park named ABC, is required to be protected by green fencing. The length of the side BC is 293. If the length of side AB is a perfect square, the length of the side AC is a power of two (2), and the length of side AC is twice the length of side AB. Determine how much fencing is required to cover the triangular park.

ABC is a triangle and BC =  293 
Let the length of AB = $$x^2$$
The length of AC = $$2^y$$
AC = 2AB
$$2^y = 2.x^2$$
$$2^{y-1} = x^2$$
$$2^{y-1}$$ is a perfect square when y is odd.
Sum of any two sides of a triangle should be larger than the third side. Therefore,
$$2^y + x^2$$ > 293, 293 + $$2^y$$ > $$x^2$$ and 293 + $$x^2$$ > $$2^y$$
y > 8
If y = 9, AC = 512, x = 16; satisfies above equations.
If y = 11, AC = 2048, x = 32; doesn't satisfy above equations.
Therefore, AB = 256 and AC = 512
Fencing required = 256 + 512 + 293 = 1061
Answer is option D.