How many 5-centimeter squares are needed to completely cover a 1-meter square without overlapping?

Imagine lining up these 5cm squares to form a rectangle of dimensions 5cm x 1m. We need 100/5 = 20 squares.

Next imagine stacking up these 5cm x 1m rectangles to form a square of dimensions 1m x 1m. We need 100/5 = 20 rectangles.

Each rectangle contains 20 squares, and we need 20 of them. Hence the number of 5cm squares required is 20*20 = 400.

A shortcut is to see that the smaller square is similar to the bigger square, with length scale factor 20. Since area scale factor is the length scale factor squared, we see that the area of the large square is 20^2 times larger than the smaller square. Therefore we need 20^2 small squares to make up the same area.

I hope this helps you :)

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