Question

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

Answer 1

Hint: Use formula, Area of parallelogram $ = $base $ \times $ height.

 Given, the area of parallelogram is $1470c{m^2}$and $AB = 35cm$ and $AD = 49cm$ are bases of the parallelogram.
$DL$ and $BM$ are the corresponding heights of the parallelogram.
We know that, Area of parallelogram $ = $base $ \times $ height. Using this formula for finding $DL$:
$
   \Rightarrow 1470 = AB \times DL, \\
   \Rightarrow 1470 = 35 \times DL, \\
   \Rightarrow DL = 42. \\
 $
Similarly for $BM$:
$
   \Rightarrow 1470 = AD \times BM, \\
   \Rightarrow 1470 = 49 \times BM, \\
   \Rightarrow BM = 30. \\
 $
Therefore, the lengths of $DL$ and $BM$ are $42cm$ and $30cm$ respectively.
Note: There is another formula of area of parallelogram as:
Area of parallelogram $ = \frac{1}{2} \times $(product of diagonals).
We can use either formulae wherever required, as per our convenience.