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.

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.

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.

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.

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.