Terrace tiles

Mr. Novak wants to pave a terrace using two sizes of square tiles, while minimising the number of tiles. His terrace is square with a side of 3 metres. Two sides of the terrace are against the house wall. Along the walls, he wants to place small tiles, and large tiles elsewhere. He wants the tile side to be at most 55 cm.
How many tiles does he need to buy? What must be the side length of the large tiles? What must be the side length of the small tiles?

Final Answer:

n =  52
a =  54.4767 cm
b =  22.2222 cm

Step-by-step explanation:

$$\begin{gathered} d=300 \\ a<55 \\ b<55 \\ n/2\cdot a^2+n/2\cdot b^2=d^2 \\ 2d=a(n/2+1) \\ n=52 \end{gathered}$$

$a=54.476704205051=54.4767\text{cm}$

$b=22.222222222222=22.2222\text{cm}$

Try another example