Hello vjesus12.

Here, we have to calculate the area of a square, which is equal to $$A=l^2$$ where l is the length of the sides of the square. Hence, all we have to do is to find the value of l.

(1) The perimeter of the floor is a whole-number multiple of 10.

The perimeter of a square is 4*l. Here, we are told that $$4\cdot l=10\cdot n,\ \ \ where\ n\in\mathbb{Z}$$ Hence we have $$4\cdot l=10\ \ \ \Rightarrow\ \ l=\frac{5}{2}\ \ \ \Rightarrow\ \ \ \ \ A=l^2=\frac{25}{4}.$$ $$4\cdot l=20\ \ \ \Rightarrow\ \ l=5\ \ \ \Rightarrow\ \ \ \ \ A=l^2=25.$$ $$4\cdot l=40\ \ \ \Rightarrow\ \ l=10\ \ \ \Rightarrow\ \ \ \ \ A=l^2=100.$$ Since we got different answers, this statement is NOT SUFFICCIENT.

$$(2)\ \ The\ \ diagonal\ \ of\ \ the\ \ floor\ \ measures\ \ 5\sqrt{2}.$$

The diagonal of a square is given by $$d=\sqrt{l^2+l^2}=\sqrt{2l^2}=l\sqrt{2}.$$ Here, we are told that $$d=5\sqrt{2}\ \ \Rightarrow\ \ \ \ l\sqrt{2}=5\sqrt{2}\ \ \ \Rightarrow\ \ \ l=5\ \ \ \Rightarrow\ \ A=25.$$ Here, we just got one answer. therefore, this statement is SUFFICCIENT.

The correct answer to this DS question is the option B.