Question

The longer side of a parallelogram is 18 cm and the corresponding altitude is 4 cm. If the length of shorter side is 12 cm, then what is the altitude corresponding to the shorter side?

• A. 2 cm
• B. 4 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is C 6 cm

Consider parallelogram ABCD.
Length of the longer side of ABCD = AB = CD = 18 cm
Length of the altitude corresponding to the longer side of ABCD = DL = 4 cm
Length of the shorter side of ABCD = AD = BC = 12 cm
The altitude corresponding to the shorter side of ABCD is BM.

Area of a parallelogram= base $\times$ height
$⟹$ Area = AB$\times$ DL= AD $\times$ BM
$\Rightarrow 18\times 4=12\times BM$
$\Rightarrow$ $BM=\frac{18\times 4}{12}=6\text{cm}$
$\therefore$ The altitude corresponding to the shorter side of ABCD is 6 cm.