#### Answer

$w=4.5cm$
$l=7.5cm$

#### Work Step by Step

$P=2l+2w$ where $l$ = length and $w$ = width
The length of the rectangle is 3 cm greater than its width. Thus,
$l=3+w$
The perimeter of the rectangle is $24$
Substitute these values into the original equation and solve for $w$.
$24=2l+2w
\\24=2(3+w)+2w
\\24=6+2w+2w
\\24=6+4w
\\24-6=4w
\\18=4w
\\\frac{18}{4}=\frac{4w}{4}
\\4.5=w$
The width is $4.5$ cm.
Substitute $w$ into the equation for $l$:
$l=3+w
\\l=3+4.5
\\7.5=l$
The length is $7.5$ cm.
To confirm that this is indeed correct, substitute the values of $l$ and $w$ into $P$.
$P=2(7.5)+2(4.5)$
$P=15+9$
$P=24cm$