Given: Two isosceles triangles have equal vertical angles and their areas are in the ratio of 36:25.
To find: Ratio of their corresponding heights.
Suppose ∆ABC and ∆PQR are two isosceles triangles with .
Now, AB = AC and PQ = PR
In ∆ABC and ∆PQR,
∴ ∆ABC ∆PQR (SAS Similarity)
Let AD and PS be the altitudes of ∆ABC and ∆PQR, respectively.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.
Hence, the ratio of their corresponding heights is 6 : 5.