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Answer:(i)x=6, y=2√5, z=3√5 (ii)x=5, y=2√5, z=3√5
Step-by-step explanation:
(i)As per similarity of triangle,
ΔBDC≅ΔABC
So, DC/BC=BC/AC
⇒5/z=z/9
z²=45
z=3√5
Now, ΔADB≅ΔABC
AD/AB=AB/AC
⇒4/x=x/9
x²=36
x=6
AD/BD=AB/BC
4/y=6/3√5
y=2√5
(ii)Similarly,
ΔPSQ≅ΔPQR
PS/PQ=PQ/PR
4/6=6/4+x
16+4x=36
x=5
PQ/QS=PR/QR
6/y=9/z
2z=3y--------(1)
RS/QS=SQ/PS
5/y=y/4
y²=20
y=2√5
From (1),
2z=3(2√5)
z=3√5
Hope it helps you..