The ratio of the areas of two triangles is 1 : 2 and the ratio of their bases is 3 : 4. What will be the ratio of their height?
Let the bases of the triangles be 3x and 4x units.
Heights of the triangles be a and b units respectively.
Then, Ratio of their areas = $$\dfrac{1}{2}\times3x\times a : \dfrac{1}{2}\times4x\times b = 3a : 4b$$
Given, $$3a :Â 4b = 1 :Â 2$$
=> $$3a\times2 = 4b\times1 => 6a = 4b$$
=> $$\dfrac{a}{b} = \dfrac{4}{6} = \dfrac{2}{3}$$
Therefore, Their heights will be in the ratio 2 :Â 3.
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