Question

Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{two}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{be}5x\mathrm{cm}\mathrm{and}3x\mathrm{cm},\mathrm{respectively}. \\ \mathrm{Then},\mathrm{its}\mathrm{perimeter}=2\left(5x+3x\right)\mathrm{cm} \end{gathered}$$
$=16x\mathrm{cm}$
$$\begin{gathered} \therefore 16x=64 \\ \Rightarrow x=\frac{64}{16} \\ \Rightarrow x=4 \\ \therefore \mathrm{One}\mathrm{side}\Rightarrow \left(5\times 4\right)\mathrm{cm}=20\mathrm{cm} \\ \mathrm{Other}\mathrm{side}\Rightarrow \left(3\times 4\right)\mathrm{cm}=12\mathrm{cm} \end{gathered}$$