Step-by-step explanation:
[tex]\triangle HFM \sim \triangle PST... (Given) \\\\
\therefore \frac{HF}{PS} = \frac{FM}{ST} = \frac{HM}{PT}...(csst) \\ \\ \therefore \frac{30}{PS} = \frac{35}{ST} = \frac{45}{9}\\ \\ \therefore \frac{30}{PS} = \frac{35}{ST} = \frac{5}{1} \\ \\ \therefore \frac{30}{PS} = \frac{5}{1} \\ \\ \therefore PS = \frac{30}{5} \\ \\\boxed{ \therefore PS = 6 }\\ \\ \because \: \frac{35}{ST} = \frac{5}{1} \\ \\ \therefore \: ST = \frac{35}{5} \\ \\ \boxed{\therefore \: ST = 7} \\ \\ perimeter \: of \: \triangle PST \\ = 9 + 7 + 6 \\ = 22 \: units[/tex]
