Q. 75.0( 4 Votes )
Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. find the ratio of their corresponding heights.
Let ABC and DEF are two isosceles triangles with AB =AC and DE = DF and ∠A = ∠D
Now, let AM and DN are their respective altitudes or heights.
Let ABC and DEF
∠A = ∠D [given]
∴ ABC ~DEF [by SAS similarity]
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.
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