Question

A farmer's rectangular field is 40 m longer than it is wide. The perimeter of the field is 580 m. What are the dimensions of the field? Set up an equation, and solve.

Answer 1

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:

`2(x+x+40)=580`

Next, we solve for x

`\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}`

Therefore, the dimensions of the field are:

`\begin{gathered} \text{Wid}\mathrm{}th,\text{ x=125 meters} \\ \text{Length, x+40 =125+40 =165 meters} \end{gathered}`

The rectangular field is 125 meters wide and 165 meters long.