Question

Write a simplified expression that Northern expression that repression the length of each side of the fieldNorth Side:____________________South Side:____________________East Side:____________________West Side:_______________________

Answer 1

The North side is equal to the South side, as we have a rectangle for the field.

Then we can write:

`\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}`

With the value of x we can calculate all four sides:

`N=(3x+1)+(2x+4)+(5x-2)=10x+3=10\cdot4+3=40+3=43`
`S=N=43`
`E=2x+(2x+5)=4x+5=4\cdot4+5=16+5=21`

We know that West = East, but we will add it independently to verify it is correct:

`W=(2x+1)+3x=5x+1=5\cdot4+1=20+1=21`

Answer:

North side = 43

South side = 43

East side = 21

West side = 21