jmc

From the problem statement, we construct the following diagram: Using the Pythagorean Theorem: $(AD{)}^2=(AC{)}^2+(CD{)}^2$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$ Substituting $(AB{)}^2+(BC{)}^2$ for $(AC{)}^2$: $(AD{)}^2=(AB{)}^2+(BC{)}^2+(CD{)}^2$ Plugging in the given information: $(AD{)}^2=(18{)}^2+(21{)}^2+(14{)}^2$ $(AD{)}^2=961$ $(AD)=31$ So the perimeter is $18+21+14+31=84$, and the answer is $\boxed{84}$.