$a)\left|BC\right|=a=10$  

$\left|AB\right|=a=10$  

$\left|AC\right|=a\sqrt{2}=10\sqrt{2}$  

$O=10+10+10\sqrt{2}=\underline{\underline{20+10\sqrt{2}}}$  

$P=\frac{1}{2}\cdot a\cdot a=\frac{1}{2}\cdot 10\cdot 10=\frac{1}{2}\cdot 100=\underline{\underline{50}}$  

$b)\left|BC\right|=a\sqrt{2}=12$  

$a\sqrt{2}=12\mid :\sqrt{2}$  

$a=\frac{12}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{2}=6\sqrt{2}$  

$\left|AC\right|=\left|AB\right|=6\sqrt{2}$  

$O=12+6\sqrt{2}+6\sqrt{2}=\underline{\underline{12+12\sqrt{2}}}$  

$P=\frac{1}{2}\cdot a\cdot a=\frac{1}{2}\cdot 6\sqrt{2}\cdot 6\sqrt{2}=3\sqrt{2}\cdot 6\sqrt{2}=18\sqrt{4}=18\cdot 2=\underline{\underline{36}}$

$c)\alpha +\alpha +{90}^o={180}^o\mid -{90}^o$  

$2\alpha ={90}^o\mid :2$  

$\alpha ={45}^o$  

$\left|AB\right|=a\sqrt{2}=14$  

$a\sqrt{2}=14\mid :\sqrt{2}$  

$a=\frac{14}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{14\sqrt{2}}{2}=7\sqrt{2}$  

$O=7\sqrt{2}+7\sqrt{2}+14=\underline{\underline{14\sqrt{2}+14}}$   

$P=\frac{1}{2}\cdot 7\sqrt{2}\cdot 7\sqrt{2}=\frac{1}{2}\cdot 49\sqrt{4}=\frac{1}{2}\cdot 49\cdot 2=\underline{\underline{49}}$