[tex]\mbox{tg }60^\circ=\frac{5}{z}\\\sqrt{3}=\frac{5}{z}\quad|\cdot{z}\\z\sqrt{3}=5\quad|:\sqrt{3}\\z=\frac{5}{\sqrt{3}}\\z=\frac{5\sqrt{3}}{3}[/tex]
[tex]\sin60^\circ=\frac{5}{t}\\\frac{\sqrt{3}}{2}=\frac{5}{t}\\t\cdot\sqrt{3}=2\cdot5\\t\sqrt{3}=10\\t=\frac{10}{\sqrt{3}}\\t=\frac{10\sqrt{3}}{3}[/tex]
[tex]\mbox{tg }45^\circ=\frac{5}{y}\\1=\frac{5}{y}\quad|\cdot{y}\\y=5[/tex]
[tex]\sin45^\circ=\frac{5}{x}\\\frac{\sqrt{2}}{2}=\frac{5}{x}\\x\cdot\sqrt{2}=2\cdot5\\x\sqrt{2}=10\quad|:\sqrt{2}\\x=\frac{10}{\sqrt{2}}\\x=\frac{10\sqrt{2}}{2}\\x=5\sqrt{2}[/tex]
[tex]L=z+y+x+t\\L=\frac{5\sqrt{3}}{3}+5+5\sqrt{2}+\frac{10\sqrt{3}}{3}=\frac{15\sqrt{3}}{3}+5+5\sqrt{2}=5\sqrt{3}+5+5\sqrt{2}[/tex]
[tex]P=\frac{(z+y)5}{2}\\P=\frac{(\frac{5\sqrt{3}}{3}+5)5}{2}=\frac{\frac{25\sqrt{3}}{3}+25}{2}=\frac{25\sqrt{3}}{6}+\frac{25}{2}[/tex]
