Question

In triangle 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.

Answer 1

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