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Length = 8m
perimeter = 2(l+b)
               =28m .
diagonal divides the rectangle shaped room into two equal right-angled triangles
  So, the diagonal will be the hypotenuse of the right-angled triangle .
      We know that (hypotenuse)²=(side)²+(side)²
     So, (hypotenuse)²=(8)²+(6)² 
   therefore , the total distance covered by the cat = 28m+10m=38m
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Perimeter of rectangle is 2lb and total length of 4 walls is 28m
diagonal of this is sq root of 8^2+6^2 which is 10 m and hence the total distance ran by rat is 38 m.