10) From a square with a side of $10 \mathrm{~cm}$, the four corners are cut in such a way as to obtain a regular octagon. The side of the octagon is 
(A) $4 \mathrm{~cm}$
(B) $10 \cdot(\sqrt{2}-1) \mathrm{cm}$
(C) $3 \sqrt{2} \mathrm{~cm}$
(D) $5 \mathrm{~cm}$
(E) the above answers are all incorrect.

![](https://cdn.mathpix.com/cropped/2024_04_17_58bef2a2a14f9f84b61bg-2.jpg?height=235&width=242&top_left_y=114&top_left_x=1192)
10) The answer is $\mathbf{( B )}$.

Let $x$ be the length of the side of the octagon. We must have $x+2 \frac{x}{\sqrt{2}}=10 \mathrm{~cm}$, from which $x=\frac{10}{1+\sqrt{2}}=$ $10(\sqrt{2}-1) \mathrm{cm}$.