Question

ABC IS AN ISOSCELES TRIANGLE WITH AB=AC=2A AND BC = A . IF AD IS PERPENDICULAR TO BC FIND THE LENGTH OF AD..

Answer 1

let the perpendicular ad bisects bc
therefore length of bd=1/2 a
according to pythagoras theorem
hypotenuse square=Base square +perpendicular square
ac square=1/2 bc square +ad square
4a^2 =a^2/4+ad square
therefore ad square =4a^2- a^2/4
therefore ad=a root 15/2

Answer 2

In an isosceles ΔABC in which AB=AC=2a units, BC=a units  

 

AD is the altitude. Therefore, D is the midpoint of BC  

 

⇒BD=  2 a

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We have two right triangles:  ΔADB and ΔADC  

 By Pythagoras theorem,  

 AB  2 =BD  2  +AD  2

 (2a)  2  =(  2 a ​  )  2  +AD  2    

(2a)  2  =  4 a 2  +AD  2

 AD  2  =  4  16a  2  −a  2  =  4 15a  2

 AD=  2 a  15 ​  

​Hence, the length of the altitude AD is   1/2  root 15  units.