[tex]P=60 \text{ m}=2l+2w\\
l=x \text{ m}\\
A=lw\\\\
2l+2w=60\\
2w=60-2l\\
w=30-l \\w=30-x\\\\
A=x\cdot(30-x)\\
A=30x-x^2\\\\
A_{max}=A\left(\dfrac{x_2-x_1}{2}\right)\\
x(30-x)=0\\
x=0 \vee x=30\\
A_{max}=A\left(\dfrac{30-0}{2}\right)\\
A_{max}=A(15)\\
A_{max}=30\cdot15-15^2\\
A_{max}=450-225\\
\boxed{A_{max}=225 \text{ m}^2}
[/tex]