we draw a picture
red line is the Rob's road traveled 6ft, 6ft and diagonal
we can calculate the diagonal using pythagoras because the shape of the walk is a right triangle
[tex]a^2+b^2=h^2[/tex]where a and b are legs of the triangle and h the hypotenuse, replacing the values of the legs
[tex]6^2+6^2=d^2[/tex]simplify
[tex]\begin{gathered} 36+36=d^2 \\ 72=d^2 \end{gathered}[/tex]and solve for diagonal
[tex]\begin{gathered} d=\sqrt[]{72} \\ d=6\sqrt[]{2} \end{gathered}[/tex]now sum the walked sides
[tex]\begin{gathered} 6+6+6\sqrt[]{2} \\ =12+6\sqrt[]{2}\approx20.5 \end{gathered}[/tex]Rob walks 20.5 feet
