Let the width of the rectangular field = x meters
Since the field is 40 m longer than it is wide,
• Length of the rectangular field = x+40 meters
Given, the perimeter of the field = 580 m
Perimeter of a rectangle = 2(Length + Width)
Substitution of the given values gives:
[tex]2(x+x+40)=580[/tex]Next, we solve for x
[tex]\begin{gathered} 2(2x+40)=580 \\ \text{Divide both sides by 2} \\ 2x+40=290 \\ 2x=290-40 \\ 2x=250 \\ \text{Divide both sides by 2} \\ x=125\text{ meters} \end{gathered}[/tex]Therefore, the dimensions of the field are:
[tex]\begin{gathered} \text{Wid}\mathrm{}th,\text{ x=125 meters} \\ \text{Length, x+40 =125+40 =165 meters} \end{gathered}[/tex]The rectangular field is 125 meters wide and 165 meters long.
