question_answer 19)

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

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.