The areas of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio :

Answer: Option C

Let the length of sides of the two triangles be a₁ and a₂ respectively and their altitudes be h₁ and h₂ respectively.
Then,
$$\begin{array}{rl}& \iff \frac{\frac{\sqrt{3}}{4}{a}_1^2}{\frac{\sqrt{3}}{4}{a}_2^2}=\frac{25}{36}\\ & \Rightarrow {\left(\frac{a_1}{a_2}\right)}^2={\left(\frac{5}{6}\right)}^2\\ & \Rightarrow \frac{a_1}{a_2}=\frac{5}{6}\end{array}$$
And
$$\begin{array}{rl}& \iff \frac{\frac{1}{2}\times a_1\times h_1}{\frac{1}{2}\times a_2\times h_2}=\frac{25}{36}\\ & \Rightarrow \frac{5}{6}\times \frac{h_1}{h_2}=\frac{25}{36}\\ & \Rightarrow \frac{h_1}{h_2}=\frac{25}{36}\times \frac{6}{5}\\ & \Rightarrow \frac{h_1}{h_2}=\frac{5}{6}\end{array}$$