∆ABC~∆DEF and their areas are respectively 64 cm2 and 121cm2. If EF = 15.4cm, find BC.

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∆ABC~∆DEF and their areas are respectively 64 cm2 and 121cm2. If EF = 15.4cm, find BC.

Answer:

Given,

∆ ABC ~ ∆ DEF.

The ratio of the areas of these triangles will be equal to the ration of squares of their corresponding sides.

$\eqalign{ & \frac{ar(\vartriangle ABC)}{ar(\vartriangle DEF)} = \frac{{B{C^2}}}{{E{F^2}}} \cr & BC = 'x'cm \cr}$

$\begin{array}{l} \frac{{64}}{{121}} = \frac{{{x^2}}}{{{{(15.4)}^2}}}\\ {x^2} = \frac{{64 \times 15.4 \times 15.4}}{{121}}\\ x = \sqrt {\frac{{(64 \times 15.4 \times 15.4)}}{{121}}} \\ x = \frac{{8 \times 15.4}}{{11}}\\ x = 11.2\\ \therefore BC = 11.2cm \end{array}$