Two similar triangles have perimeters 30 cm and 45 cm. If a side of the smaller triangle is 8 cm, find the corresponding side of the larger triangle.

Two similar triangles have areas 36 cm² and 64 cm². If the perimeter of the smaller is 27 cm, find the perimeter of the larger.

The areas of two similar triangles are 81 cm² and 49 cm². If a side of the larger triangle is 27 cm, find the corresponding side of the smaller.

Assertion: all squares are similar to one another. Reason: in any two squares the corresponding angles are equal and the corresponding sides are proportional. State whether both are true and whether the reason explains the assertion.

In triangle ABC, D and E are points on AB and AC such that DE is parallel to BC. If AD : DB = 2 : 3 and the area of triangle ADE is 16 cm², find the area of triangle ABC.

The corresponding sides of two similar triangles are in the ratio 3 : 5. Find the ratio of their areas.

In triangle ABC, DE is parallel to BC. If AD = 4 cm, AB = 10 cm and DE = 6 cm, find BC.