Q2 of 95 Page 6

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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