One of the heights of the triangle breaks it into triangles with perimeters of 25 cm and 29 cm
| July 23, 2021 | education
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.
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