question_answer 14)

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of parallelogram is \[\text{1470 c}{{\text{m}}^{\text{2}}}\] and \[\text{AB}=\text{35 cm}\]and \[\text{AD}=\text{49 cm}\], find the length of BM and DL.

Answer:

                Area of parallelogram ABC \[=\text{base}\times \text{height}\]               \[\text{= AD  }\!\!\times\!\!\text{  BM}\] \[\Rightarrow \]               \[\text{1470 = 49  }\!\!\times\!\!\text{  BM}\] \[\Rightarrow \]               \[\text{BM = }\frac{\text{1470}}{\text{49}}\text{ cm}\] \[\Rightarrow \]               \[\text{BM = 30 cm}\] Hence, the length of BM is 30 cm. Again, area of parallelogram ABCD \[=\text{base}\times \text{height}\]                 \[\text{= AB  }\!\!\times\!\!\text{  DL}\]                 \[\Rightarrow \]               \[\text{1470 = 35  }\!\!\times\!\!\text{  DL}\] \[\Rightarrow \]               \[\text{DL = }\frac{\text{1470}}{\text{35}}\text{ cm}\] \[\Rightarrow \]               \[\text{DL = 42 cm}\] Hence, the length of DL is 42 cm.