Question

If the altitudes of two similar triangles are of ratio 2:3 what is the ratio of corresponding median ​

Answer 1

Answer:

If two triangles are similar, then, ratio of their corresponding sides=ratio of their corresponding medians=ratio of their corresponding altitudes     (equation 1)

AD/PS = 2/3

ar(ABC)/ar(PQR) = (AD/PS)^2    (from 1)

                           = (2/3)^2

                           = 4/9

ar(ABC)/ar(PQR) = 4/9

Ratio of their corresponding medians = 2/3    (from 1)