What is the maximum possible area of an equilateral triangle inside a rectangle R that has a perimeter of 30 $$cm$$?

Statement 1: The area of the rectangle R is 54 $$cm^2$$.

Statement 2: The length of the diagonals of R is $$\sqrt{\ 117}\ cm$$.

The key in data sufficiency questions is to determine whether the answer is fixed; we need not find the answer itself, but eliminate if there are other possibilities.

Before considering the statements we know that $$2(l+b)$$ equals 30, hence $$l+b$$ equals 15 cm

The rectangle R could be of multiple forms, so we might not be able to find the exact triangle; hence, the maximum area can not be uniquely determined. 

Let's consider statement 1:

It give us the information that $$lb$$ equals 54, along with $$l+b$$ equals 15, which would give us a quadratic equation, which can be used to find the values of both $$l$$ and $$b$$
Can we determine the triangle's maximum area once we know the exact side lengths of the triangle?
We can see that in order for the triangle to be of maximum length, we would want the side length to be maximum. Since that can be difficult to do, we can also try to maximize the base and height of the triangle. We can take the side length such that the base can be placed on the longer side, and the height would be equal to the smaller side of the rectangle. This would give us the maximum area possible. 

Hence, Statement 1 alone is sufficient. 

Let's consider statement 2:

This gives us $$l^2+b^2=117$$; this, along with the value of $$l+b$$ we have before considering the statements, which can also be used to uniquely determine the dimensions of the rectangle. 

After this, the same process would follow as we did for statement 1

Hence, Statement 2 alone is also sufficient. 

Therefore, Option B is the correct answer.