Answer:
The width of rectangle is [tex]W=\frac{108}{13}\ cm[/tex] or [tex]8\frac{4}{13}\ cm[/tex]
Step-by-step explanation:
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
where
L is the length of rectangle
W is the width of rectangle
we have
[tex]P=26\ cm\\L=(x+4)\ cm\\W=12x\ cm[/tex]
substitute
[tex]26=2(x+4+12x)[/tex]
solve for x
[tex]26=2(13x+4)[/tex]
[tex]26=26x+8[/tex]
[tex]26x=26-8[/tex]
[tex]26x=18[/tex]
[tex]x=\frac{18}{26}[/tex]
simplify
[tex]x=\frac{9}{13}[/tex]
Find the width of rectangle
[tex]W=12x\ cm[/tex]
substitute the value of x
[tex]W=12(\frac{9}{13})=\frac{108}{13}\ cm[/tex]
Convert to mixed number
[tex]\frac{108}{13}\ cm=\frac{104}{13}+\frac{4}{13}=8\frac{4}{13}\ cm[/tex]
