The sum of angles in a triangle is 180°. Therefore, the third angle = 180° - 30° - 60° = 90°.

Area ratio = (r1/r2)² = (3/5)² = 9/25.

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2:3)² = 4:9.

If the ratio is 2:1, then the sides of the second triangle are 3*2, 4*2, and 5*2, which gives 6 cm, 8 cm, and 10 cm.

In a 45-45-90 triangle, the legs are equal and each leg = hypotenuse/√2 = 10/√2 = 5√2 cm.

The ratio of similarity is 6/3 = 2. Therefore, the sides are 3*2 = 6 cm, 4*2 = 8 cm, 5*2 = 10 cm.

Diagonal = √(width² + height²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.