Correct. The area enclosed by the fence is $\displaystyle{\left({40}+{2}{x}\right)}{\left({20}+{2}{x}\right)}={1},{500}\usepackage{cmbright}\Huge\$ .

Multiply out: $\displaystyle{800}+{120}{x}+{4}{{x}}^{{2}}={1},{500}\usepackage{cmbright}\Huge\$ , so $\displaystyle-{700}+{120}{x}+{4}{{x}}^{{2}}={0}\usepackage{cmbright}\Huge\$

Divide by 4 and rearrange terms: $\displaystyle{{x}}^{{2}}+{30}{x}-{175}={0}\usepackage{cmbright}\Huge\$

Use the Quadratic Formula:

$\displaystyle{x}=\frac{{-{30}\pm\sqrt{{{{30}}^{{2}}-{4}\cdot{1}\cdot{\left(-{175}\right)}}}}}{{{2}\cdot{1}}}=\frac{{-{30}\pm\sqrt{{{1},{600}}}}}{{2}}\usepackage{cmbright}\Huge\$

So $\displaystyle{x}=\frac{{-{30}\pm{40}}}{{2}}={5}\usepackage{cmbright}\Huge\$ or $\displaystyle-{35}\usepackage{cmbright}\Huge\$ . The negative solution is impossible, so $\displaystyle{x}={5}\usepackage{cmbright}\Huge\$ feet.