One of the heights of the triangle breaks it into triangles with perimeters of 25 cm and 29 cm, find this height if the perimeter of the triangle is 40 cm.
1. Vertices of the triangle A, B, C. BH – height. The perimeters of triangles ABH and BCH are 25 and 29 centimeters, respectively.
2. The perimeter of the triangle ABH = BH + AH + AB = 25 centimeters.
The perimeter of the triangle ВСН = ВН + СН + ВС = 29 centimeters.
3. We add these expressions:
2ВН + AB + ВС + СН + АН = 54 centimeters.
3. CH + AH = AC.
2BH + AB + BC + AC = 54 centimeters.
(AB + BC + AC) is the perimeter of the ABC triangle (equal to 40 centimeters).
2BH + 40 = 54 centimeters.
BH = 7 centimeters.
Answer: The height of the HV is 7 centimeters.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.