Júlio performs multiplications using only the squares of numbers. He has to calculate the product $85 \times 135$. To do this, he draws a rectangle of $85 \times 135 \mathrm{~mm}$ and, in this rectangle, he draws the largest possible square; he does the same in the remaining rectangle and so on. In this way, he obtains eight squares which he then sums. Draw the figure made by Júlio and write $85 \times 135$ as the sum of eight squares:

$$
85 \times 135=85^{2}+\ldots
$$
The largest square in the rectangle of $85 \times 135$ is the one measuring $85 \times 85$. This leaves a rectangle of $50 \times 85$, in which the largest square measures $50 \times 50$. Continuing this process, we obtain

$$
85 \times 135=85^{2}+50^{2}+35^{2}+15^{2}+15^{2}+5^{2}+5^{2}+5^{2}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-062.jpg?height=611&width=951&top_left_y=731&top_left_x=630)