the perimeter of the complex figure is 64 in in the area is 186 squared to inches find the lengths of Q and M

According to the image the addition between q and m should be 14 in, thos would be your first equation
[tex]Q+M=14in[/tex]The second equation could be obtained when finding the area of the figure after dividing the figure into 2 rectangles.
[tex](7in)\cdot(14in)+(11in\cdot M)=186in^2[/tex]solve the second equation for M
[tex]\begin{gathered} 98in^2+11Min^{}=186in^2 \\ 11Min^{}=(186-98)in^2 \\ 11Min^{}=88in^2 \\ M=\frac{88in^2}{11in} \\ M=8in \end{gathered}[/tex]replace the value of M into the first equation
[tex]\begin{gathered} Q+M=14in \\ Q+8in=14in \\ Q=14in-8in \\ Q=6in \end{gathered}[/tex]