Question

The sides of a rectangle are in the ratio 4 : 5. Find its sides if the perimeter is 90 cm.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{side}\mathrm{be}x\mathrm{cm}\mathrm{and}ycm. \\ \mathrm{So},\mathrm{we}\mathrm{have}: \\ 2\left(x+y\right)=90 \\ \mathrm{Sides}\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{ratio}4:5. \\ \therefore y=\frac{5x}{4} \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}: \\ 2\left(x+\frac{5x}{4}\right)=90 \\ \frac{4x+5x}{4}=45 \\ 9x=180 \\ x=20 \\ \therefore y=\frac{5\times 20}{4}=25 \\ \mathrm{Thus},\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{will}\mathrm{be}20\mathrm{cm}\mathrm{and}25\mathrm{cm}. \end{gathered}$$