Question

If the perimeters of two similar triangles is 30 cm and 24 cm and the length of one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.

Answer 1

$$\begin{gathered} \mathrm{Let}△\mathrm{ABC}\mathrm{and}△\mathrm{PQR}\mathrm{be}\mathrm{two}\mathrm{similar}\mathrm{triangles}\mathrm{of}\mathrm{perimeters}{p}_{1}and{p}_2\mathrm{respectively}. \\ \mathrm{Also}\mathrm{let}\mathrm{AB}=12\mathrm{cm},p_1=30\mathrm{cm}\mathrm{and}{p}_2=24\mathrm{cm}. \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}: \\ △\mathrm{ABC}~△\mathrm{PQR} \\ \Rightarrow \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{\mathrm{AC}}{\mathrm{PR}}=\frac{p_1}{p_2}\left[\mathrm{ratio}\mathrm{of}\mathrm{corresponding}\mathrm{sides}\mathrm{of}\mathrm{similar}\mathrm{triangles}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{their}\mathrm{perimeters}\right] \\ \Rightarrow \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{p_1}{p_2} \\ \Rightarrow \frac{12}{\mathrm{PQ}}=\frac{30}{24} \\ \Rightarrow \mathrm{PQ}=\frac{12\times 24}{30}=\frac{48}{5} \\ \Rightarrow \mathrm{PQ}=9.6\mathrm{cm} \end{gathered}$$