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Question
In triangle BMP and CNR it is given that PB= 5 cm, MP = 6cm BM = 9 cm and NR = 9cm. If ΔBMP∼ ΔCNR then find the perimeter of ΔCNR
Solution
When two triangles are similar, then the ratios of the lengths of their corresponding sides are proportional.
Here, ΔBMP ~ ΔCNR
∴` (BM)/(CN)=(BP)/(CR)=(MP)/(NR)` ...........(1)
NOW`(BM)/(CN)=(MP)/(NR)` [𝑈𝑠𝑖𝑛𝑔 (1)]
⇒ `CN=(BMxxNR)/(MP)=(9xx9)/6=13.5 cm`
𝐴𝑔𝑎𝑖𝑛, `(BM)/(CN)=(BP)/(CR)` [𝑈𝑠𝑖𝑛𝑔 (1)]
⇒ `CR=(BPxxCN)/(BM)=(5xx13.5)/9=7.5 cm`
Perimeter of ΔCNR = CN + NR + CR = 13.5 + 9 + 7.5 = 30 cm
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