In a triangle with sides of 25 cm and 40 cm, the bisector of the angle between these sides is drawn. It divides the third side into a segment, the smaller of which is 15 cm. Find the perimeter of the triangle.
To solve the problem, we apply the property of the bisector of the angle of a triangle, according to which it divides the opposite side of the triangle into segments proportional to the adjacent sides.
BC / BM = AC / AM.
25/15 = 40 / AM.
AM = 15 * 40/25 = 24 cm.
Then the length of the segment AB = AM + BM = 24 + 15 = 39 cm.
Determine the perimeter of the triangle.
Ravs = (AB + BC + AC) = (39 + 25 + 40) = 104 cm.
Answer: The perimeter of the triangle is 104 cm.
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