18.2. A segment 20 cm long is divided into two segments, and a square is constructed on each of them as a side. Find the lengths of the sides of these squares, if the difference in the areas of the squares is $120 \mathrm{~cm}^{2}$.

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\text { (7-8 grades) }
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18.2. Let the side of the larger square be $x$. Then the side of the smaller square is $20-x$. According to the problem, we have:

$$
x^{2}-(20-x)^{2}=120, \text { hence } 40 x=520, \text { i.e., } x=13 .
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Answer: The sides of the squares are 13 cm and 7 cm.