# 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 $DL$.

Last updated date: 22nd Mar 2023

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Answer

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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.

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.

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