Question

The longer side of a parallelogram is 81 cm and the corresponding altitude is 16 cm. If the length of shorter side is 24 cm, what is the altitude corresponding to the shorter side?

• A. 36 cm
• B. 48 cm
• C. 54 cm
• D. 24 cm

Answer 1

The correct option is C 54 cm


Consider ABCD.
Length of the longer side of ABCD = AB = CD = 81 cm
Length of the altitude corresponding to the longer side of ABCD = DL = 16 cm
Length of the shorter side of ABCD = AD = BC = 24 cm
The altitude corresponding to the shorter side of ABCD is BM.

$\text{Area of a parallelogram}=\text{base}\times \text{height}$
$⟹\text{Area}=AB\times DL=AD\times BM$
$\Rightarrow 81\times 16=24\times BM$
$\Rightarrow$ $BM=\frac{81\times 16}{24}=54\text{cm}$
$\therefore$ The altitude corresponding to the shorter side of ABCD is 54 cm.