The vertex angle of two isosceles triangles are equal and their areas are in ratio 64:225. Find the ratio of their corresponding altitudes.
Answers
Given : The vertex angle of two isosceles triangles are equal and their areas are in ratio 64:225
To find : ratio of their corresponding altitudes.
Solution:
Vertex angle of two isosceles triangles are equal
=> Both isosceles triangles are similar
( let say two triangle ABC & PQR
∠A = ∠P
∠B = ∠C = (180 - A)/2
∠Q = ∠R = (180 - P)/2
∠A = ∠P => ∠B = ∠C = ∠Q = ∠R =
Hence ΔABC ≈ Δ PQR
For similar triangles
Ratio of area of triangle = Ratio of corresponding sides²
=> 64 : 225= Ratio of corresponding sides²
=> 8 : 15= Ratio of corresponding sides
For similar triangles
Ratio of corresponding altitudes = Ratio of corresponding sides
=> Ratio of corresponding altitudes = 8 : 15
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