If the areas of two similar triangles are 360 cm² and 250 cm² and if one side of the first triangle is 8 cm, find the length of the corresponding side of the second triangle.

Let the corresponding side of the second 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 sides.

$\therefore \dfrac{\text{Area of } △$1}{\text{Area of } △2} = \dfrac{(\text{Side of } △1)^2}{(\text{Side of } △2)^2} \\[1em] \Rightarrow \dfrac{360}{250} = \dfrac{8^2}{x^2} \\[1em] \Rightarrow x^2 = \dfrac{64 \times 250}{360} \\[1em] \Rightarrow x^2 = \dfrac{16000}{360} \\[1em] \Rightarrow x^2 = \dfrac{1600}{36} \\[1em] \Rightarrow x = \sqrt{\dfrac{1600}{36}} \\[1em] \Rightarrow x = \dfrac{40}{6} \\[1em] \Rightarrow x = \dfrac{20}{3} = 6\dfrac{2}{3}.

Hence, the length of corresponding side of second triangle is $6\dfrac{2}{3}$ cm.