Answer
width = 40 meters
length = 75 meters
Work Step by Step
Let $x$ be the width of the field.
Hence,
Width = $x$
Length = $2x-5$
Since the field is enclosed by a $230$-meter fence. Then this means that $230$ meters is the perimeter of the field.
The formula for the perimeter of a rectangle is given by the equation:
$P = 2L + 2W$
Substitute the expressions for length and width, as well as the value of the perimeter:
$$230 = 2(2x-5) + 2x$$
Evaluate the equation.
$$230 = 2(2x-5) + 2x$$ $$230= 4x - 10 + 2x$$ $$230 = 6x - 10$$
Add $10$ to both sides:
$$230 + 10 = 6x - 10 + 10$$ $$240 = 6x$$
Divide both sides by $6$:
$$\frac{230}{6} = \frac{6x}{6}$$ $$40 = x$$
Thus,
width = $40$ meters
length = $2x-5$
$=2(40)-5$
$=75$ meters
