Question

In Fig. 42, ABCD is a parallelogram in which AD = 21 cm, DH =18 cm and DK = 27 cm.
The perimeter of the parallelogram is

(a) 105 cm (b) 84.5 cm (c) 169 cm (d) 52.5 cm

Answer 1

Area of a parallelogram = Base $\text{×}$ Height
$$\begin{gathered} AB\times DH=AD\times DK \\ \Rightarrow AB\times 18=21\times 27 \\ \Rightarrow AB=\frac{21\times 27}{18}=\frac{63}{2}=31.5\mathrm{cm} \end{gathered}$$
Here, ABCD is a parallelogram, so AB = CD and AD = BC.
Therefore
Perimeter of parallelogram ABCD = 2(AB + AD)
= 2(31.5 + 21)
= 105 cm
Hence, the correct option is (a).