Find the perimeter of a triangle if its two sides are 20 and 30 cm and the bisector the angles

Find the perimeter of a triangle if its two sides are 20 and 30 cm and the bisector the angles between them divides the third side into segments, the smallest of which is 10 cm

Let the ВСD triangle be given, where ВС = 20 cm, СD = 30 cm.
СK – bisector of angle <BCD, СK = 10 cm. ВD = ВK + KD. We need to find the ВD and the perimeter.
According to the theorem “on the bisector”, which divides the opposite side of the ВD into segments ВC and CD proportional to the other two sides of the ВC and СD:
ВK: KD = ВС: СD,
substitute the given values:
(10: CD = 20: 30), CD = 10 * 30: 20 = 15 (cm),
СD = VK + KD = 10 cm + 15 cm = 25 cm.
Perimeter = Sun + СD + ВD = 20 cm + 30 cm + 25 cm = 75 cm.
Side ВD = 25 cm, and perimeter 75 cm.