Terrace tiles

Mr. Novák wants to pave the terrace with tiles of two sizes to be as small as possible. Its terrace is square with a side 3 meters long. There is a wall of the house on two sides of the terrace. Next to the wall, he wants to put small tiles, the rest large. He wants square tiles with a side of maximally 55 cm.
How many tiles does he have to buy? How long must large tiles have? How long must small tiles have?

Final Answer:

n =  52
a =  54.4767 cm
b =  22.2222 cm

Step-by-step explanation:

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

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

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

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