The North side is equal to the South side, as we have a rectangle for the field.
Then we can write:
[tex]\begin{gathered} \text{North}=\text{South} \\ (3x+1)+(2x+4)+(5x-2)=(2x+5)+(6x-3)+(x+5) \\ 3x+2x+5x+1+4-2=2x+6x+x+5-3+5 \\ 10x+3=9x+7 \\ 10x-9x=7-3 \\ x=4 \end{gathered}[/tex]
With the value of x we can calculate all four sides:
[tex]N=(3x+1)+(2x+4)+(5x-2)=10x+3=10\cdot4+3=40+3=43[/tex][tex]S=N=43[/tex][tex]E=2x+(2x+5)=4x+5=4\cdot4+5=16+5=21[/tex]
We know that West = East, but we will add it independently to verify it is correct:
[tex]W=(2x+1)+3x=5x+1=5\cdot4+1=20+1=21[/tex]
Answer:
North side = 43
South side = 43
East side = 21
West side = 21
