SOLUTION: In triangle ABC, AB = AC, and line segment AD bisects line BC. If AB = 6 and BC = 4, then what is the length of AD ?

Algebra ->  Geometry-proofs -> SOLUTION: In triangle ABC, AB = AC, and line segment AD bisects line BC. If AB = 6 and BC = 4, then what is the length of AD ?       Log On


   

Question 597574: In triangle ABC, AB = AC, and line segment AD bisects line BC. If AB = 6 and BC = 4, then what is the length of AD ?
Answer by w_parminder(53) About Me  (Show Source):
You can put this solution on YOUR website!
Triangle ABC is an isosceles triangle as AB = AC, therefore the median AD is perpendicular to the base BC. So, in triangle ABD, angle ADB = 90 degree. In triangle ABD, AB = 6, BD = BC/2 i.e. BD = 2. We can apply pythagoras theorem,i.e.
P%5E2%2BB%5E2=H%5E2
AD%5E2%2BBD%5E2=AB%5E2
AD%5E2%2B2%5E2=6%5E2
AD%5E2%2B4=36
AD%5E2=36-4
AD%5E2 = 32
AD = √32
AD ≈ 5.657