Question

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

• A. 30 cm, 42 cm
• B. 72 cm ,56 cm
• C. 42 cm, 30 cm
• D. 56 cm, 72 cm

Answer 1

The correct option is A 30 cm, 42 cm

Given: Area of parallelogram = 1470 $c{m}^2$
We have AB = 35 cm and AD = 49 cm.
Area of a parallelogram = base $\times$ height
Considering AB as base and DL as the corresponding height, we get
1470 = 35 $\times$ DL
$\Rightarrow$ $DL=\frac{1470}{35}=42cm$

Considering AD as base and BM as corresponding height, we get
$\Rightarrow$ $1470=49\times BM$
$\Rightarrow$ $BM=\frac{1470}{49}=30cm$
Thus, the lengths of BM and DL are 30 cm and 42 cm respectively.