# In a triangle BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm.

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

Solution:

When two triangles are similar, then the ratios of the lengths of their corresponding sides are proportional.
Here, △BMP ∼ △CNR

$\therefore \frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{BP}}{\mathrm{CR}}=\frac{\mathrm{MP}}{\mathrm{NR}} \quad \ldots(1)$

Now, $\frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{MP}}{\mathrm{NR}} \quad[$ Using $(1)]$

$\Rightarrow \mathrm{CN}=\frac{\mathrm{BM} \times \mathrm{NR}}{\mathrm{MP}}=\frac{9 \times 9}{6}=13.5 \mathrm{~cm}$

Again, $\frac{\mathrm{BM}}{\mathrm{CN}}=\frac{\mathrm{BP}}{\mathrm{CR}} \quad[$ Using (1) $]$

$\Rightarrow \mathrm{CR}=\frac{\mathrm{BP} \times \mathrm{CN}}{\mathrm{BM}}=\frac{5 \times 13.5}{9}=7.5 \mathrm{~cm}$

Perimeter of △CNR = CN + NR + CR = 13.5 + 9 + 7.5 = 30 cm

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