For the cicle with intersecting chords the relation between the length of segments of chords is,
[tex]KL\cdot ZL=WL\cdot PL[/tex]
Substitute the values in the equation and solve for x.
[tex]\begin{gathered} 2\cdot(3x-2)=x\cdot5 \\ 6x-4=5x \\ 6x-5x=4 \\ x=4 \end{gathered}[/tex]
So value of x is 4.
The equation for the length of chord KZ is,
[tex]\begin{gathered} KZ=KL+LZ \\ =2+3x-2 \\ =3x \end{gathered}[/tex]
Substitute the value of x in equation to determine the length of KZ.
[tex]\begin{gathered} KZ=3\cdot4 \\ =12 \end{gathered}[/tex]
So answer is 12.
