Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. find the ratio of their corresponding heights.

Question

Philoid · Accepted Answer

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]

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)]