What is the source of this question? I ask because instead of saying "faces" (which belong to 3-D figures), the question should have said "sides".
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The question stem tells us that "a circle with a radius of x cm is inscribed inside a quadrilateral so that it touches all internal faces of the quadrilateral."
The kinds of quadrilaterals in which a circle can be inscribed (such that all four sides of the quadrilateral touch the circle) include: rhombi, kites, and trapezoids. (Squares are a type of rhombus. A non-square rhombus is like a "pushed over" square).
(1) gives us no quantitative information, no numbers. And we don't get any quantitative informaton in the question stem either. Thus, (1) is clearly insufficient.
From (2), we get the perimeter of the quadrilateral. The area of a quadrilateral--and, therefore, the area of a circle inscribed in a quadrilateral--is maximized when its sides are equalized AND when they meet at right angles.
Thus, if their perimeters are the same, then the area of a square is bigger than the area of a "pushed over" square. This is because as we push the square over, its height decreases (accordingly, the diameter of the circle decreases). Insufficient.
(1) + (2):
(1) tells us that the diagonals bisect each other. To bisect is to cut in half. The diagonals of squares and other rhombi cut each other in half; the diagonals of kites and trapezoids do not.
So, now we know that the shape can be a square or a "pushed over" square, and that the sides are all equal. But, again, because the area of a quadrilateral is maximized when the sides meet at right angles, the circle will be bigger if it were inscribed in a square (than if it were inscribed in a "pushed over" square).
Choose E.
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