ΔABC and ΔDEF are similar triangles and their areas are 49 cm² and 144 cm² respectively. If EF = 16.80 cm, then find BC.

9.8 cm

Concept used:

When two triangles are similar, then the ratio of area of both triangles is proportional to the square of the asides of the ratio of their corresponding sides.

⇒ \(\frac{AB}{DE}\) = \(\frac{BC}{EF}\) = \(\frac{AC}{DF}\) = \(\sqrt {area\,of\,Δ\,ABC\,/\,area\,of\,Δ\,DEF }\)

⇒  \(\frac{BC}{EF}\) = \(\sqrt {area\,of\,Δ\,ABC\,/\,area\,of\,Δ\,DEF }\)

⇒  BC = \(\frac{7}{12}\) x 16.80

⇒  BC = 9.8 cm

Therefore, length of BC is 9.8 cm.