B3 In the figure, three squares are inscribed in a right-angled triangle (see figure). Calculate the side $x$ of the third square exactly.

(6 points)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-05.jpg?height=371&width=739&top_left_y=1077&top_left_x=1178)
B3. We supplement the diagram with points $A, B, C, D$ and $E$ and determine that triangles $A B C$ and $C D E$ are similar. We write the appropriate ratio of corresponding sides $\frac{|A B|}{|B C|}=\frac{|C D|}{|D E|}$. We insert $\frac{6}{4}=\frac{10}{x-10}$ and calculate $6 x-60=40$, so $x=\frac{50}{3}$.

Determining that triangles ABC and CDE are similar ................................... 1 point

Considering the theorem that the quotient of corresponding sides is constant............ 1 point

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![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-13.jpg?height=66&width=1685&top_left_y=1937&top_left_x=228)