Triangle ABC and A1B1C1 are similar. AB = 12cm, A1B1 = 8cm, B1C1 = 7cm, A1C1 = 5cm

Triangle ABC and A1B1C1 are similar. AB = 12cm, A1B1 = 8cm, B1C1 = 7cm, A1C1 = 5cm. Find BC and AC of triangle ABC.

The data for the condition of the triangles are similar. The proportionality of the sides follows from the similarity of triangles. We find the proportionality coefficient:
k = AB / A1B1 = 12/8 = 1.5.
Knowing the proportionality coefficient and the sides of the A1B1C1 triangle, we find the unknown sides of the ABC triangle:
BC = 1.5 * B1C1 = 10.5 (cm);
AC = 1.5 * A1C1 = 7.5 (cm).
Answer: BC length 10.5 cm, speaker length 7.5 cm.