145. The Partitioned Corner. One of the corners of a rectangular room is partitioned off using two identical screens, each 4 meters long. How should the screens be placed to maximize the area of the partitioned section?

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
145. The fenced area has the shape of a quadrilateral, two sides of which, emanating from the vertex opposite to[^29]

![](https://cdn.mathpix.com/cropped/2024_05_21_2b40d984baf9da275c68g-122.jpg?height=255&width=265&top_left_y=318&top_left_x=901)

the right angle, are equal to each other. From four quadrilaterals congruent to the given one, a regular octagon can be formed. Among such octagons, the one with the maximum area is the regular octagon. Therefore, one-fourth of this regular octagon represents the quadrilateral of maximum area, which is $8(\sqrt{2}+1)$ m$^2$. Thus, the screens should be placed such that each forms an equilateral triangle with the wall and the bisector of the right angle, with the side length equal to the length of the screen.

$[\Phi$. Hawthorn, N. M. M., 19, 322 (March 1945).]