Correct option is : (1) 30
\(\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1\)
\(\frac{3}{a}+\frac{5}{b}=1 \Rightarrow b=\frac{5 a}{a-3}, a>3\)
\(A=\frac{1}{2} a b=\frac{1}{2} a \frac{5 a}{(a-3)}=\frac{5}{2} \cdot \frac{a^{2}}{a-3}\)
\(=\frac{5}{2}\left(\frac{a^{2}-9+9}{a-3}\right)\)
\(=\frac{5}{2}\left(a+3+\frac{9}{a-3}\right)\)
\(=\frac{5}{2}\left(a-3+\frac{9}{a-3}+6\right) \geq 30\)
