Correct. The area of the scarf is $\displaystyle{4}\cdot{1}={4}\usepackage{cmbright}\Huge\$ . Adding a border of width x, the new area of the scarf is $\displaystyle{\left({4}+{2}{x}\right)}{\left({1}+{2}{x}\right)}\usepackage{cmbright}\Huge\$ . The area of the border is given by the equation $\displaystyle{\left({4}+{2}{x}\right)}{\left({1}+{2}{x}\right)}-{\left({4}\right)}{\left({1}\right)}={6}\usepackage{cmbright}\Huge\$ , which can be rewritten as the trinomial $\displaystyle{0}={4}{{x}}^{{2}}+{10}{x}-{6}\usepackage{cmbright}\Huge\$ . Solving this trinomial yields $\displaystyle{x}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ or $\displaystyle{x}=-{3}\usepackage{cmbright}\Huge\$ . Since -3 does not make sense in this context, the width of the border must be $\displaystyle\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ foot, or 6 inches.