**Quote:**

If the two statements were for different sides of the rectangle, I agree that statement C is correct.

The statements refer to different sides of the rectangle, when combined, because just one side of the rectangle can not be equal and be twice longer than the side of the square AT THE SAME TIME.

i.e. The system

*b* =

*a**b* = 2

*a* is NOT possible for positive

*a* and

*b* (it's possible only if

*a* =

*b* = 0).

Let's take a look at the both statements combined once again.

**(1) A side of the rectangle equals to a side of the square.**This statement transforms into *b* = *a* (we chose side

*b*, but could have chosen side

*c*. Considering the denotation, it does NOT affect the reasoning).

**(2) A side of the rectangle is twice greater than a side of the square.**We already know that *b* = *a*, so *c* = 2*a*. Note, that since

*b* =

*a*, then side

*c* is twice longer than side

*b* in the rectangle. So

*c* is the larger side of the rectangle.

The areas are

*a*² vs. bc =

*a* × (2

*a*) = 2

*a*².

So the area of the rectangle is greater.