Tiles

The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?

Correct answer:

a₁ =  15 cm
b₁ =  1350 cm

Step-by-step explanation:

$$\begin{gathered} a_0=15\text{ cm } \\ {x}_1=1,y_1=90 \\ {x}_2=2,y_2=45 \\ {x}_3=3,y_3=30 \\ {x}_4=5,y_4=18 \\ {x}_5=6,y_5=15 \\ {x}_6=9,y_6=10 \\ {a}_1=a_0\cdot 1=15\cdot 1=15\text{ cm} \end{gathered}$$

$b_1=a_0\cdot 90=15\cdot 90=1350\text{ cm}$

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