Can two art albums, each $22 \mathrm{~cm}$ wide, and a cookbook $25 \mathrm{~cm}$ wide fit into an advertising bag that is $28 \mathrm{~cm}$ wide, if each of the three books is individually $1.5 \mathrm{~cm}$ thick?
The "circumference of the mouth" of the advertising bag is $2 \cdot 28 = 56 \text{ cm}$. If we can arrange the books such that the "combined cross-sectional" circumference is at most $56 \text{ cm}$, then we can slide them into the bag. From experience, we know that a good arrangement is when the largest book, in this case, the cookbook, is placed in the center. The two art books are then placed symmetrically below and above it. The front view of this arrangement is shown in Figure 1; the circumference is: $K = 2 \cdot 22 + 2 \cdot 1.5 + 4 \cdot x$, where $x = 1.5 \sqrt{2}$, so $K = 47 + 6 \sqrt{2} \approx 55.485356$, which means the books do not fit into the advertising bag.
![](https://cdn.mathpix.com/cropped/2024_05_02_e82d6f5b53fb8e626647g-1.jpg?height=394&width=676&top_left_y=552&top_left_x=708)

$25 \text{ cm}$