# 7.1. Condition:

A carpenter took a wooden square and cut out 4 smaller equal squares from it, the area of each of which was $9 \%$ of the area of the larger one. The remaining area of the original square was $256 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_ecded04271ea1e1132a0g-13.jpg?height=612&width=605&top_left_y=662&top_left_x=791)

Find the side of the original square. Express your answer in centimeters.
Answer: 20

Solution.

Let the side of the larger square be 10x. The area of the smaller square is $9 \%$ of the area of the larger square, which is $9 / 100 \cdot 100 x^{2}=9 x^{2}$. After removing four smaller squares, the remaining area is $100 x^{2}-4 \cdot 9 x^{2}=64 x^{2}=256 \text{ cm}^{2}$. Therefore, $x^{2}=4$. Hence, $x=2$ cm, and the entire side is $10 x=20$ cm.