Step-by-step explanation
The picture tells us that sides OV and VU have the same length. With this information we can construct an equation for x:
![7x+2=3x+10](https://img.qammunity.org/2023/formulas/mathematics/college/e5zbdlua7znmkxoogg5pxg20lie2j43nsi.png)
Let's substract 3x and 2 from both sides of this equation:
![\begin{gathered} 7x+2-3x-2=3x+10-3x-2 \\ 4x=8 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/outah0sxh2aqcq7mxt57dzoualjgay8hyr.png)
Then we can divide both sides by 4:
![\begin{gathered} (4x)/(4)=(8)/(4) \\ x=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/k5ta8f3dn2zdmj018233ttby97cxf295zn.png)
Then the length of VU is given by:
![3x+10=3*2+10=16](https://img.qammunity.org/2023/formulas/mathematics/college/m3vg78xr6hn89fv4zovajpa989mogc15qg.png)
Answer
Then the answer is 16.