In the given figure <ABC=900 And BD ⊥ AC. If AB=5.7cm, BD=3.8cm and CD=4.4cm, Find length of side BC.
Given that,
∠ABC=900&BD⊥AC
and
AB=5.7cm
BD=3.8cm
CD=4.4cm
BC=?
Let AD=ycm and BC=xcm
Then,InΔABD
By pythagoras theorem,
AB2=AD2+DB2
(5.7)2=y2+(3.8)2
32.49=y2+13.3
y2=32.49−13.3
y2=19.19
y=4.38cm
Now, InΔABC
By Pythagoras theorem,
AC2=AB2+BC2
(y+4.4)2=(5.7)2+x2
(4.38+4.4)2=32.49+x2
(8.78)2−32.49=x2
x2=77.87−32.49
x2=45.38
x=6.73cm
BC=x=6.73cm
Hence, this is the answer.