Q. 85.0( 3 Votes )

# 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.

Answer :

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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