If areas of similar triangles ΔABC and ΔDEF are x² cm² and y² cm² respectively, and EF = a cm, then BC( in cm) is:

$\frac{ax}{y}$

According to the concept,

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

Calculations

ΔABC is similar to ΔDEF

So, (\(\frac{BC}{EF}\))²  = \(\frac{area\; of\; ΔABC }{area\; of\; ΔDEF}\)

⇒ (\(\frac{BC}{a}\))²  = (\(\frac{x}{y}\))²

⇒ \(\frac{BC}{a}\) = \(\frac{x}{y}\)

⇒ BC = \(\frac{ax}{y}\)

Therefore, BC is \(\frac{ax}{y}\) cm.