Answer:
In right-angled triangle DAB, \[A{{B}^{2}}+A{{D}^{2}}=B{{D}^{2}}\] \[\Rightarrow \] \[{{40}^{2}}+A{{D}^{2}}={{41}^{2}}\] \[\Rightarrow \] \[A{{D}^{2}}={{41}^{2}}-{{40}^{2}}\] \[\Rightarrow \] \[A{{D}^{2}}=1681-1600\] \[\Rightarrow \] \[A{{D}^{2}}=81\] \[\Rightarrow \] \[AD=9\] \[\therefore \] Perimeter of the rectangle \[=2(AB+AD)\] \[=2(40+9)\] \[=2(49)=\text{98 cm}\] Hence, the perimeter of the rectangle is 98 cm.
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