Given that △s ABC and PQR are similar. Find :

(i) the ratio of the area of △ABC to the area of △PQR if their corresponding sides are in the ratio 1 : 3.

(ii) the ratio of their corresponding sides if area of △ABC : area of △PQR = 25 : 36.

(i) We know that, the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

$\therefore \dfrac{\text{Area of △ABC}}{\text{Area of △PQR}} = \dfrac{(1)^2}{(3)^2} \\[1em] = \dfrac{1}{9} \\[1em] = 1 : 9.$

Hence, the ratio of area of △ABC to △PQR = 1 : 9.

(ii) Let the corresponding sides be in ratio x : y.

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

$\therefore \dfrac{\text{Area of △ABC}}{\text{Area of △PQR}} = \dfrac{x^2}{y^2} \\[1em] \Rightarrow \dfrac{25}{36} = \dfrac{x^2}{y^2} \\[1em] \Rightarrow \Big(\dfrac{5}{6}\Big)^2 = \Big(\dfrac{x}{y}\Big)^2 \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{5}{6} \\[1em] \Rightarrow x : y = 5 : 6.$

Hence, the ratio of corresponding sides of △ABC and △PQR = 5 : 6.