If the perimeter of the triangle
ABC is 192m,
AH is perpendicular on BC.
what is the length of AH? Given that
AB = 64m , AC = 48m
Answers
Given : perimeter of the triangle ABC is 192m
AH is perpendicular on BC.
AB = 64m , AC = 48m
To Find : AH
Solution:
perimeter of the triangle ABC is 192m
=> s = semi perimeter = 192/2 = 96 m
AB + BC + AC = Perimeter
Third side BC = 192 - 64 - 48 = 80 m
Area of triangle using Heron's Formula
= √96(96 - 64)(96-48)(96-80)
= √96(32)(48)(16)
= √(32*3)(32)(16*3)(16)
= 32 * 3 * 16
Area of Triangle = (1/2) * base * height
= (1/2) * BC * AH
= (1/2) * 80 * AH
= 40 * AH
40 * AH = 32 * 3 * 16
=> AH = 32 * 3 * 16/ 40
=> AH = 38.4 m
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