Q8 of 95 Page 6

The areas of two similar triangles are 100 cm2 and 49 cm2, respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other.


Given: Let ΔABC = 100cm2 and ΔDEF = 49cm2


Let AM = 5cm


Here, ΔABC and ΔDEF are similar triangles


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


⇒∠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)]






⇒DN = 3.5cm


The height of the other altitude is 3.5cm


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