∆ABC and ∆DEF are similar and their areas are respectively 0.64 $$m^2$$​ and 0.0121 $$m^2$$​. If EF = 0.154 m, then BC is:

Correct option is C

Given:
∆ABC ~ ∆ DEF
ar(ABC)=0.64 $$m^2$$​​
ar(DEF)=0.0121 $$m^2$$​​
EF=0.154m
Formula Used:
​$$\frac{\text{ar}(\triangle ABC)}{\text{ar}(\triangle DEF)} = \frac{AB^2}{DE^2} = \frac{BC^2}{EF^2} = \frac{AC^2}{DF^2}$$ 

Solution:

$$\frac{\text{ar}(\triangle ABC)}{\text{ar}(\triangle DEF)} = \frac{BC^2}{EF^2} \\\frac{0.64}{0.0121} = \frac{BC^2}{(0.154)^2} \\\sqrt{\frac{0.64}{0.0121}} = \frac{0.8}{0.11} \\BC = \frac{8}{1.1} \times 0.154 \\BC = 8 \times 0.14 = 1.12 \, \text{m}$$​