The bisector BH is drawn in an isosceles triangle ABC with base AC. Find the perimeter
| April 19, 2021 | education
The bisector BH is drawn in an isosceles triangle ABC with base AC. Find the perimeter of a triangle BHC if ab = 10 cm, ac = 8 cm, bh = 6 cm.
Since BH is the bisector of the angle opposite to the base of an isosceles triangle, this bisector is also the height and median of the triangle. Then AH = CH = AC / 2 = 8/2 = 4 cm, and the triangles ABН and СВН are rectangular.
The length of the side BC = AB = 10 cm, since the triangle ABC is isosceles.
The perimeter of the ВНС triangle is: Rvns = BC + CH + ВН = 10 + 4 + 6 = 20 cm.
Answer: The perimeter of the ВНС triangle is 20 cm.
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