The perimeter of a figure is the sum of all its sides.
In the given figure, we have two unknown sides, let's call them a and b:
Also, we can say that:
[tex]\begin{gathered} w+a+u=y\text{ Equation 1} \\ b+x=v+z\text{ Equation 2} \end{gathered}[/tex]
By replacing the known values, we can find a and b:
[tex]\begin{gathered} a=y-w-u \\ a=12-4-5=12-9=3inches \\ \\ b=v+z-x \\ b=7+4-7=4inches \end{gathered}[/tex]
So, the perimeter is given by:
[tex]\begin{gathered} P=a+b+u+v+w+x+y+z \\ P=3+4+5+7+4+7+12+4 \\ P=46\text{ inches} \end{gathered}[/tex]
The answer is B. 46 inches
