Given two isosceles triangles have equal angles and their areas are in the ratio 16 : 25.

We know that SAS similarity criterion states that if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

In ΔABC and ΔDEF,

if and ∠A = ∠D, then ΔABC ~ ΔDEF

We know that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes.

∴ AG: DH = 4: 5