Question

hey guys im class 10 student plz help me this

Answer 1

BD : CD = 3:2
BD/ BC = 3/5
BD = (3/5)BC
CD = (2/5) BC
in triangle ABD
( AD) ^2 = (AB) ^2 - (BD) ^2 ..........(1)
in triangle ACD
(AD)^2 = (AC) ^2 - (CD)^2 ...........(2)
from EQ 1 and 2
(AB) ^2 - (BD)^2 = ( AC) ^2 - (CD) ^2
put the value of BD and CD
( AB)^2 - ( 3/5 BC) ^2 = (AC) ^2 - ( 2/5 BC)^2
( AB) ^2 - ( AC) ^2 = 9/25 ( BC) ^2 - 4/25 ( BC)^2
(AB) ^2 - ( AC) ^2 = 5/25 ( BC) ^2
( AB) ^2 - ( AC)^2 = 1/5 ( BC) ^2