Q. 25.0( 3 Votes )

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

Answer :

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)

∠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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