Q. 114.5( 2 Votes )
The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. If the altitude of the first triangle is 6.3 cm, find the corresponding altitude of the other.
Given: Let ABC = 81cm2 and DEF = 49cm2
Let AM = 6.3cm
Here, ABC and DEF 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]
We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.
⇒DN = 4.9cm
Height of the other altitude is 4.9cm
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