Given a triangle ABC, the perimeter of which is 42 cm. On the AC side, point M is taken, so that the perimeter

Given a triangle ABC, the perimeter of which is 42 cm. On the AC side, point M is taken, so that the perimeter of triangle ABM and triangle BCM are 32 cm and 35 cm, respectively. Find the length of the ВM segment.

P (triangle ABC) = AB + BC + CA = 42 cm; also by condition it is specified that AC = AM + MS, because point M is taken on the AC side; P (triangle ABM) = AB + BM + MA = 32 cm; P (triangle BMC) = BC + CM + MB = 35 cm; then P (triangle ABC) = P (triangle ABM) – MB + P (triangle BMC) – MB; We substitute the given values into the equations of the perimeter of the triangle ABC, the unknown side of the MВ is denoted by the variable x:

42 = 32 – x + 35 – x;

2x = 32 + 35 – 42;

2x = 67 – 42;

2x = 25;

x = 25: 2;

x = 12.5 (cm) – ВM side.

Answer: ВM = 12.5 cm.