question_answer

Find the area of a rectangular plot one side of which is 48 cm and its diagonal is 50 m.

Answer:

Let the other side be x metres. Since ΔABC is a right triangle. Therefore, \[A{{C}^{2}}=A{{D}^{2}}+C{{D}^{2}}\] \[{{50}^{2}}={{48}^{2}}+{{x}^{2}}\] \[{{x}^{2}}={{\left( 50 \right)}^{2}}{{\left( 48 \right)}^{2}}\] \[{{x}^{2}}=\left( 50+48 \right)\left( 5048 \right)\] \[{{x}^{2}}=98\times 2\] \[{{x}^{2}}={{14}^{2}}\] x = 14                                                                                                                                      Thus, the other side of the rectangle is 14 m. ∴ Area of the rectangle\[~=(48\times 14){{m}^{2}}=672{{m}^{2}}\]