The perimeter of Marlene's house is the total distance around the edge of her house.
The perimeter can be calculated thus:
[tex]\begin{gathered} (2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)+(x-2)+(x)+(2x+2)+ \\ (\frac{1}{2}x-4)+(x-2)+(x-2)+(x) \end{gathered}[/tex]
Collect like terms
[tex]\begin{gathered} (2x+x+\frac{1}{2}x+x+x+x+2x+\frac{1}{2}x+x+x+x)\text{ +} \\ (-10-2-4-2-2+2-4-2-2) \\ =12x-26 \end{gathered}[/tex]
Therefore, the algebraic expression representing the perimeter of Marlene's house is
[tex]12x-26[/tex]
