In triangles BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If $Δ B M P \sim Δ C N R$ then find the perimeter of $Δ C N R$ .

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Solution

When two triangles are similar, then the ratios of the lengths of their corresponding sides are proportional.

Here, $Δ B M P \sim Δ C N R$

Therefore,
$\frac{B M}{C N} = \frac{B P}{C R} = \frac{M P}{N R}$ .....(1)

Now, $\frac{B M}{C N} = \frac{M P}{N R}$
[ Using (1) ]

⇒ $C N = B M \times \frac{N R}{M P}$
$= 9 \times \frac{9}{6} = 13.5$

$\frac{B M}{C N} = \frac{B P}{C R}$
[Using (i) ]

⇒ $C R = B P \times \frac{C N}{B M}$
= $5 \times 13. \frac{5}{9} = 7.5$

Perimeter of $Δ C N R = C N + N R + C R$
$= 13.5 + 9 + 7.5$
$= 30 c m$

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

In triangles BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If $Δ B M P \sim Δ C N R$ then find the perimeter of $Δ C N R$ .