Question

In a triangle BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If △BMP ∼ △CNR, then find the perimeter of the △CNR

Answer 1

When two triangles are similar, then the ratios of the lengths of their corresponding sides are proportional.
Here, △BMP ∼ △CNR
$$\begin{gathered} \therefore \frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{BP}}{\mathrm{CR}}=\frac{\mathrm{MP}}{\mathrm{NR}}....\left(1\right) \\ \mathrm{Now},\frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{MP}}{\mathrm{NR}}\left[\mathrm{Using}\left(1\right)\right] \\ \Rightarrow \mathrm{CN}=\frac{\mathrm{BM}\times \mathrm{NR}}{\mathrm{MP}}=\frac{9\times 9}{6}=13.5\mathrm{cm} \\ \mathrm{Again},\frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{BP}}{\mathrm{CR}}\left[\mathrm{Using}\left(1\right)\right] \\ \Rightarrow \mathrm{CR}=\frac{\mathrm{BP}\times \mathrm{CN}}{\mathrm{BM}}=\frac{5\times 13.5}{9}=7.5\mathrm{cm} \end{gathered}$$
Perimeter of △CNR = CN + NR + CR = 13.5 + 9 + 7.5 = 30 cm