Question

The perimeter of a parallelogram is 102 cm. If one side is greater than the other by 9 cm, find the lengths of all sides of the parallelogram.

Answer 1

Dear Student,

$$\begin{gathered} letlength=landbreadth=b \\ Given, \\ l=9+b \\ 2\left(l+b\right)=102........\left(i\right) \\ nowputtingvalueoflinequation\left(i\right) \\ 2\left(9+b+b\right)=102 \\ 9+2b=51 \\ 2b=51-9 \\ 2b=42 \\ b=21cm \\ l=b+9=21+9=30cm \\ henceinparalle\log ramoppositesidesareequal \\ \mathbf{}\mathit{h}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathbf{}\mathit{l}\mathit{e}\mathit{n}\mathit{g}\mathit{t}\mathit{h}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{t}\mathit{w}\mathit{o}\mathbf{}\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathit{s}\mathbf{=}\mathbf{30}\mathbf{}\mathit{c}\mathit{m}\mathbf{} \\ \mathit{b}\mathit{r}\mathit{e}\mathit{a}\mathit{d}\mathit{t}\mathit{h}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{t}\mathit{w}\mathit{o}\mathbf{}\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathit{s}\mathbf{}\mathbf{=}\mathbf{21}\mathbf{}\mathit{c}\mathit{m}\mathbf{} \end{gathered}$$

Regards