6.2. Lines parallel to the sides of a square form a smaller square, the center of which coincides with the center of the original square. It is known that the area of the cross formed by the smaller square (see the figure on the right) is 17 times the area of the smaller square. How many times is the area of the original square larger than the area of the smaller square?
Answer. 81 times.

Solution. Let the square have dimensions of 1 cm $\times 1$ cm, and the larger square have dimensions of $n$ cm $\times n$ cm. Then the area of the cross is $(2 n-1)$ cm $^{2}$ (the vertical column has dimensions $n \times 1$, the horizontal row has dimensions $1 \times n$, and the area of the square is counted twice). From the equation $2 n-1=17$, we get that $n=9$. Therefore, the area of the square is $9 \times 9=81$ cm $^{2}$.

Comment. The correct answer was obtained by trial and error - 5 points.

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