If ∆ ABC ∼ ∆ XYZ, AB = 6 cm, XY = 8 cm, YZ = 12 cm and ZX = 16 cm, then find the perimeter of ∆ ABC.

Correct option is C

Given:

​$$(\triangle ABC \sim \triangle XYZ)$$

AB = 6 cm, XY = 8 cm, YZ = 12 cm, ZX = 16 cm

Find perimeter of $$\triangle$$​ABC.

Concept Used:

In similar triangles, corresponding sides are proportional:
​$$\frac{AB}{XY}=\frac{BC}{YZ}=\frac{CA}{ZX}=k$$​​

Perimeter $$P_{ABC}$$​ = AB + BC + CA.

Solution:

k=$$\frac{AB}{XY}=\frac{6}{8}=\frac{3}{4}$$​​

BC = k$$\times YZ = \frac{3}{4}\times 12 = 9\ \text{cm},$$​

CA = k $$\times ZX = \frac{3}{4}\times 16 = 12\ \text{cm}$$​​
P$$_{ABC}$$=AB + BC + CA = 6 + 9 + 12 = 27 cm