Question

The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.

Short answer

The length of the field is 160 yards and the width is 120 yards.

Step-by-step solution

Step 1. Given Information 

• The perimeter of the field is 560 yards.
• The length of the field is 40 yards more than the width of the field.

Step 2. Define the Variables

• Let the width of the field is w.
• So, the length of the field is $w+40$yards.

Step 3. Use the Perimeter Formula

• Substitute $P=560$and $l=w+40$in the formula of the perimeter of a rectangle, $P=2l+2w$and solve to find the unknown variable.

$$\begin{gathered} 560=2\left(w+40\right)+2w \\ 560=4w+80 \\ 4w=480 \\ w=120 \end{gathered}$$

• So, the width of the field is 120 yards.

Step 4. Find the Length

• Substitute $w=120$into $l=w+40$and find the length of the field.

$$\begin{gathered} l=120+40 \\ =160 \end{gathered}$$

• So, the length of the field is 160 yards.

Step 5. Conclusion

The length of the field is 160 yards and the width is 120 yards.