First we need to think how the blocks would be arranged. 30=2×3×5, so we can have 2×15, 3×10 or 5×6.
If we decide on the 2x15 arrangement, we divide the length or width of the large rectangle by 2 and then the other dimension of the big rectangle by 15. The same idea applies to 3×10 and 5×6. This gives us 6 possible solutions.
Now we look at the dimensions of the large rectangle to find out what would the best arrangement to fit the sides.
Let’s take an example. If we use 3×10 block arrangement and divide the length by 3 we get 70.5/3=23.5cm. And then we divide the width by 10 to get 52/10=5.2cm. So the size of each block is 5.2×23.5=122.2cm², and 30 of these makes 3666cm². The area of the large rectangle is 52×70.5=3666cm² so the whole area is covered with no gaps. This is one solution using 5.2×23.5 cm blocks arranged 10 by 3.
Now let’s try another arrangement: 6×5, where the blocks have dimensions 70.5/6×52/5=11.75×10.4 cm blocks.
Another arrangement is 2×15: block dimensions: 70.5/15×52/2=4.7×26 cm blocks.
The remaining three arrangements give solutions, too, but we will get fifteenths, thirds, or sixths in the measurements rather than simple decimals.