The ratio of base of two triangles is x : y and the ratio of their area is a : b.  The ratio of their corresponding altitudes is:

\(\frac{a}{x}\) : \(\frac{b}{y}\)

Base ratio ⇒  x  :   y

 Altitudes  ⇒ h₁ :   h₂

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Area  =  \(\frac{1}{2}\) xh₁  :  \(\frac{1}{2}\) yh₂ 

a : b  =  xh₁  :  yh₂

⇒ h₁ :  h₂ = \(\frac{a}{x}\)  :  \(\frac{b}{y}\)