ΔABC ~ ΔDEF and the area of ΔABC is 13.5 cm² and the area of ΔDEF is 24 cm². If BC = 3.15 cm, then the length (in cm) of EF is:

4.2

\(\frac{area\;of\;ABC}{area\;of\;DEF}\) = (\(\frac{BC}{EF}\))²

= \(\frac{13.5}{24}\) = (\(\frac{3.15}{EF}\))²

= \(\frac{13.5}{EF}\) = \(\frac{3}{4}\)

= EF = \(\frac{3.15 \;×\; 4 }{3}\) = 4.2 cm

= EF = 4.2 cm.

Therefore, EF is 4.2 cm.