The bisector of a triangle whose perimeter is 45 cm, divides its side into segments equal

The bisector of a triangle whose perimeter is 45 cm, divides its side into segments equal to 6 cm and 9 cm, calculate the lengths of the sides of the triangle.

Since the segment AM is the bisector of the angle, then by the property of the bisector:

AB / BM = AC / CM.

AB / 9 = AC / 6.

AB / AC = 3/2.

Let the length of the segment AB = 3 * X cm, then the length of the segment AC = 2 * X cm.

Side length BC = BM + CM = 9 + 6 = 15 cm.

Then the perimeter of the triangle ABC is equal to: Ravs = AB + BC + AC = 45 cm.

3 * X + 15 + 2 * X = 45.

5 * X = 30 cm.

X = 30/5 = 6 cm.

Then AB = 3 * 6 = 18 cm.

AC = 2 * 6 = 12 cm.

Answer: The lengths of the sides of the triangle are 15 cm, 12 cm, 18 cm.