ΔABC and ΔDEF are similar triangles and their areas are 49 cm2 and 144 cm2 respectively. If EF = 16.80 cm, then find BC.
Answer & explanation
Correct answer: option 2
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.