The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their:

(i) corresponding medians.

(ii) perimeters.

(iii) areas.

Let △ABC and △PQR be two similar triangles with AD and PS as perpendiculars.

So,

∠ABD = ∠PQS [As ∠ABC = ∠PQR]

∠ADB = ∠PSQ [Both = 90°]

So, △ABD ~ △PQS.

$\therefore \dfrac{AB}{PQ} = \dfrac{AD}{PS} = \dfrac{3}{5}$.

(i) The ratio between the medians of two similar triangles is same as the ratio between their sides.

Hence, the required ratio = 3 : 5.

(ii) The ratio between the perimeters of two similar triangles is same as the ratio between their sides.

Hence, the required ratio = 3 : 5.

(iii) The ratio between the areas of two similar triangles is same as the square of the ratio between their corresponding sides.

Ratio = (3)² : (5)² = 9 : 25.

Hence, the required ratio = 9 : 25.