Question

The sides of a rectangle are in the ratio 2 : 3, and its perimeter is 20 cm. Draw the rectangle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{side}\mathrm{be}x\mathrm{cm}\mathrm{and}ycm. \\ \mathrm{So},\mathrm{we}\mathrm{have}: \\ 2\left(x+y\right)=20 \\ \mathrm{Sides}\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{ratio}2:3. \\ \therefore y=\frac{3x}{2} \\ \mathrm{Putting}\mathrm{the}\mathrm{v}alue\mathit{}ofy: \\ 2\left(x+\frac{3x}{2}\right)=20 \\ \frac{2x+3x}{2}=10 \\ 5x=20 \\ x=4 \\ \therefore y=\frac{3\times 4}{2}=6 \\ \mathrm{Thus},\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{will}\mathrm{be}4\mathrm{cm}\mathrm{and}6\mathrm{cm}. \\ \mathrm{ABCD}\mathrm{is}\mathrm{the}\mathrm{rectangle}\mathrm{having}\mathrm{side}s4\mathrm{cm}\mathrm{and}6\mathrm{cm}. \end{gathered}$$