Answer:
The value of x is 4/3.
Step-by-step explanation:
It is given that triangles MOP and MNQ are similar.
The corresponding sides of similar triangles are proportional.
[tex]\frac{MQ}{MP}=\frac{MN}{MO}[/tex]
[tex]\frac{MQ}{MQ+QP}=\frac{MN}{MN+NO}[/tex]
It is given that MQ=4, QP=x, MN=6, NO=2. Put this value in the above equation.
[tex]\frac{4}{4+x}=\frac{6}{6+2}[/tex]
[tex]\frac{4}{4+x}=\frac{6}{8}[/tex]
[tex]4\times 8=6(4+x)[/tex]
[tex]32=24+6x[/tex]
[tex]32-24=6x[/tex]
[tex]8=6x[/tex]
Divide both sides by 6.
[tex]\frac{8}{6}=x[/tex]
[tex]\frac{4}{3}=x[/tex]
Therefore the value of x is 4/3.
