suppose you covered your desktop with small squares.Then you cover your desktop with large squares.Would you use more small squares or large squares?Explain
What do you think?
large squares because you wouldn't want to waste your entire time to small squares large squares would be better.
To solve this problem, we need to understand the relationship between the size of the smaller and larger squares and how they cover your desktop.
Let's assume that the smaller squares completely cover your desktop without any gaps or overlaps. Each smaller square can be placed in such a way that it perfectly fits into the available space.
Now, imagine covering your desktop with larger squares. Since the larger squares have a greater area, they will necessarily cover a larger portion of your desktop compared to the smaller squares.
To determine whether you would use more small squares or large squares, we need to consider the ratio of their sizes. If the area of one large square is equal to the combined area of several small squares, then you would use fewer large squares to cover your desktop.
In mathematical terms, let's suppose the area of one large square is L, and the area of one small square is S. If n is the number of small squares needed to cover your desktop and m is the number of large squares needed, we can write the following equation:
n * S = m * L
From this equation, we can conclude that if S/L < m/n, then you would use more large squares. But, if S/L > m/n, then you would use more small squares.
In summary, to answer the initial question of whether you would use more small squares or large squares to cover your desktop, you need to compare the ratio of their sizes. If the ratio of the larger square's area to the smaller square's area is greater than the ratio of the number of small squares to the number of large squares, you would use more small squares. Otherwise, you would use more large squares.