The perimeters of ΔABC and ΔDEF are 39.6 cm and 26.4 cm, respectively, and ΔABC ∼ ΔDEF. What is the ratio of the areas of ΔABC and ΔDEF ?
Answer & explanation
Correct answer: option 2
Point to be remembered = If two triangles are similar, the ratio of their area will be the square of the ratio of the length of their respective sides.
The perimeter of ΔABC and ΔDEF = 39.6 and 26.4 cm
According to the question
ΔABC ~ ΔDEF
= \(\frac{39.6}{26.4}\) = \(\frac{ ΔABC}{ ΔDEF}\)
= \(\frac{3}{2}\)
So,
The ratio of the areas of ΔABC and ΔDEF = \(\frac{3^2}{2^2}\) = 9 : 4