The areas of two similar triangles are 81 cm² and 49 cm² respectively. If an altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is

1. 9 cm

2. 7 cm

3. 6 cm

4. 4.5 cm

Let the altitude of bigger triangle be x cm.

We know that, the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding altitudes.

$\therefore \dfrac{\text{Area of bigger triangle}}{\text{Area of smaller triangle}} = \dfrac{(\text{Bigger triangle altitude})^2}{(\text{Smaller triangle altitude})^2} \\[1em] \Rightarrow \dfrac{81}{49} = \dfrac{x^2}{(3.5)^2} \\[1em] \Rightarrow x^2 = \dfrac{81 \times (3.5)^2}{49} \\[1em] \Rightarrow x^2 = \dfrac{992.25}{49} \\[1em] \Rightarrow x^2 = 20.25 \\[1em] \Rightarrow x = \sqrt{20.25} \\[1em] \Rightarrow x = 4.5$

Hence, altitude of the bigger triangle is 4.5 cm.

Hence, Option 4 is the correct option.