Answer
Length $=5.5$ meters.
Width $=1.5$ meters.
Work Step by Step
Let the length is $l$.
and width is $w$.
Area of the rectangle is
$A=l\cdot w$ ... (1)
From the question we have
$l=w+4$ ... (2)
$A=8$ square meters.
By using equation (1) and (2).
$8=(w+4)\cdot w$
Simplify.
$8=w^2+4w$
Subtract $8$ from both sides.
$8-8=w^2+4w-8$
$0=w^2+4w-8$
Factor.
$0=w^2+4w-8$
By using the quadratic equation solution.
$w=\frac{-4\pm \sqrt {4^2-4(1)(-8)}}{2(1)}$
$w=\frac{-4\pm \sqrt {16+32}}{2}$
$w=\frac{-4\pm \sqrt {48}}{2}$
$w=\frac{-4\pm 4\sqrt {3}}{2}$
$w=-2\pm 2\sqrt {3}$
Take positive value.
$w=-2+ 2\sqrt {3}$
$w=1.46410161514$
Round to the nearest tenth of a meter.
$w=1.5$ meters.
Plug the value of $w$ into equation (2).
$l=1.5+4$
$l=5.5$ meters.
