Raskina I.V.

The cake is packed in a box with a square base. The height of the box is half the side of this square. A ribbon of length 156 cm can be used to tie the box and make a bow on top (as shown in the left image). To tie it with the same bow on the side (as shown in the right image), a ribbon of length 178 cm is needed. Find the dimensions of the box.
![](https://cdn.mathpix.com/cropped/2024_05_06_4235c45af0b890c24417g-08.jpg?height=316&width=822&top_left_y=2541&top_left_x=617)
For the first method of tying, the ribbon encircles the box twice the length, twice the width, and four times the height, meaning its length is equal to six sides of the base plus the bow. For the second method of tying, the ribbon encircles the box twice the length, four times the width, and twice the height, meaning its length is equal to seven sides of the base plus the bow. Therefore, the difference $178-156=22$ cm in the lengths of the ribbons is equal to the side of the base of the box.

## Answer

22 cm $\times 22$ cm $\times 11$ cm.