The areas of two similar triangles are 12 cm² and 48 cm² respectively. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is:

1. 0.525 cm

2. 4.2 cm

3. 4.41 cm

4. 8.4 cm

Given,

Let, A₁ and A₂ be the areas of two triangle. h₁ and h₂ be the height of their corresponding sides.

Since the triangles are similar, the ratios of Areas of triangles is equal to squares of corresponding heights.

$\Rightarrow \dfrac{A$1}{A2} = \Big(\dfrac{h1}{h2}\Big)^2 \\[1em] \Rightarrow \dfrac{12}{48} = \Big(\dfrac{2.1}{h2}\Big)^2 \\[1em] \Rightarrow \dfrac{1}{4} = \Big(\dfrac{2.1}{h2}\Big)^2 \\[1em] \Rightarrow \sqrt{\dfrac{1}{4}} = \dfrac{2.1}{h2} \\[1em] \Rightarrow \dfrac{1}{2} = \dfrac{2.1}{h2} \\[1em] \Rightarrow h2 = 2.1 \times 2 \\[1em] \Rightarrow h2 = 4.2 \text{ cm.}

Hence, option 2 is the correct option.