The areas of two similar triangles are 81 cm² and 144 cm². If the largest side of the smaller triangle is 27 cm, then largest side of the larger triangle is:

1. 24 cm

2. 36 cm

3. 48 cm

4. none of these

Given,

Let, A₁ and A₂ be the areas of two triangle. s₁ and s₂ be the length of their corresponding sides.

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

$\Rightarrow \dfrac{A$1}{A2} = \Big(\dfrac{s1}{s2}\Big)^2 \\[1em] \Rightarrow \dfrac{81}{144} = \Big(\dfrac{27}{s2}\Big)^2 \\[1em] \Rightarrow \sqrt{\dfrac{81}{144}} = \dfrac{27}{s2} \\[1em] \Rightarrow \dfrac{9}{12} = \dfrac{27}{s2} \\[1em] \Rightarrow s2 = \dfrac{27 \times 12}{9} \\[1em] \Rightarrow s2 = \dfrac{324}{9} \\[1em] \Rightarrow s2 = 36 \text{ cm.}

Hence, option 2 is the correct option.