$\frac{\left|AB\right|}{\left|A{}^{\prime }B{}^{\prime }\right|}=\frac{\left|BC\right|}{\left|B{}^{\prime }C{}^{\prime }\right|}$  

  $\frac{18\text{cm}}{6\text{cm}}=\frac{24\text{cm}}{\left|B{}^{\prime }C{}^{\prime }\right|}$  

$18\text{cm}\cdot \left|B{}^{\prime }C{}^{\prime }\right|=6\text{cm}\cdot 24\text{cm}\mid :18\text{cm}$  

$\left|B{}^{\prime }C{}^{\prime }\right|=\frac{6\text{cm}\cdot 24\text{cm}}{18\text{cm}}=8\text{cm}$  

 

$\frac{\left|AB\right|}{\left|A{}^{\prime }B{}^{\prime }\right|}=\frac{\left|CA\right|}{\left|C{}^{\prime }A{}^{\prime }\right|}$  

$\frac{18\text{cm}}{6\text{cm}}=\frac{33\text{cm}}{\left|C{}^{\prime }A{}^{\prime }\right|}$

$18\text{cm}\cdot \left|C{}^{\prime }A{}^{\prime }\right|=6\text{cm}\cdot 33\text{cm}\mid :18\text{cm}$   

$\left|C{}^{\prime }A{}^{\prime }\right|=\frac{6\text{cm}\cdot 33\text{cm}}{18\text{cm}}=11\text{cm}$  

$O_{\text{A’B’C’}}=6\text{cm}+8\text{cm}+11\text{cm}=25\text{cm}$