# The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Given: AM = 6cm and DN = 9cm

Here, ΔABC and ΔDEF are similar triangles

We know that, in similar triangles, corresponding angles are in the same ratio.

⇒∠A = D, B = E and C = F ……(i)

In ABM and DEN

B = E [from (i)]

and M = N [each 90°]

ABC ~ DEF [by AA similarity]

So, ……(ii)

We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.

[from (ii)]

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