\(\triangle\) ABC ~ \(\triangle\) DEF and their areas are respectively 64 \(cm^2\) and 121 \(cm^2\). If EF = 15.4 cm, find BC.

Solution :

We have,    area of triangle ABC = 64 \(cm^2\)

and area of triangle DEF = 121 \(cm^2\)

We know that,

\(ar(\triangle ABC)\over ar(\triangle DEF)\) = \(({BC\over EF})^2\)

\(\implies\)  \(64\over 121\) = \(({BC\over 15.4})^2\)

\(\implies\) \(8\over 11\) = \(BC\over 15.4\)

\(\implies\) BC = 11.2 cm.