Triangles ABC and A1B1C1 are similar, with side AB corresponding to A1B1, and BC = B1C1.

Triangles ABC and A1B1C1 are similar, with side AB corresponding to A1B1, and BC = B1C1. Find the unknown sides of the triangles if AB = 8 cm, BC = 10 cm, A1B1 = 4 cm, A1C1 = 6 cm.

Let’s write down the ratio of the sides known by the condition and find the coefficient of similarity of triangles:
AB / A1B1 = 8/4 = 2 – coefficient of similarity.
Knowing the coefficient, we find the unknown sides of the triangles:
ВС / В1С1 = 2 → В1С1 = ВС / 2 = 10/2 = 5 (cm);
АС / А1С1 = 2 → АС = 2 * А1С1 = 2 * 6 = 12 (cm).
Answer: B1C1 = 5 cm, AC = 12 cm.