If areas of similar triangles ΔABC and ΔDEF are x2 cm2 and y2 cm2 respectively, and EF = a cm, then BC( in cm) is:
Answer & explanation
Correct answer: option 3
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.