The ratio of heights of two triangles is 2 : 3 and the ratio of their areas 3 : 2. The ratio of their bases is :

1. 1 : 4

2. 2 : 8

3. 9 : 4

4. 4 : 9

Let b₁ and b₂ be the bases of the triangles.

Heights (h₁ : h₂) = 2 : 3

Areas (A₁ : A₂) = 3 : 2

Area of a triangle = $\dfrac{1}{2}$ × Base × Height

$\Rightarrow \dfrac{A$1}{A2} = \dfrac{\dfrac{1}{2} \times b1 × h1}{\dfrac{1}{2} \times b2 × h2} \\[1em] \Rightarrow \dfrac{3}{2} = \dfrac{b1}{b2} \times \dfrac{h1}{h2} \\[1em] \Rightarrow \dfrac{3}{2} = \dfrac{b1}{b2} \times \dfrac{2}{3} \\[1em] \Rightarrow \dfrac{b1}{b2} = \dfrac{3 × 3}{2 × 2} \\[1em] \Rightarrow \dfrac{b1}{b2} = \dfrac{9}{4} \\[1em] \Rightarrow b1 : b2 = 9 : 4.

Hence, option 3 is the correct option.