Correct. Sophie's route is the hypotenuse of a right triangle with legs of length 15 and 20. If c is the length of her route, then by the Pythagorean Theorem, $\displaystyle{{c}}^{{2}}={{15}}^{{2}}+{{20}}^{{2}}={225}+{400}={625}\usepackage{cmbright}\Huge\$ , so $\displaystyle{c}=\sqrt{{{625}}}={25}\usepackage{cmbright}\Huge\$ yards. Since the other route would have been $\displaystyle{15}+{20}={35}\usepackage{cmbright}\Huge\$ yards long, Sophie's route is 10 yards shorter.