Answer :
Perimeter of a rectangle = 2 ( l + b )
Let the width of the rectangle be w .
Then , the length of the rectangle = w + 3
Given :-
Perimeter of the rectangle = 54 inches
Length and breadth of the rectangle :-
[tex] 54= 2(w + w + 3)[/tex]
[tex]2(w + w + 3) = 54[/tex]
[tex]2(2w + 3) = 54[/tex]
[tex]4w + 6 = 54[/tex]
[tex]4w = 54 - 6[/tex]
[tex]4w = 48[/tex]
[tex]w = \frac{48}{4} [/tex]
[tex]\color{teal}w = 12[/tex]
Which means :-
The width of this rectangle :-
[tex]\color{orange} 12 \: \: inches [/tex]
The length of this rectangle :-
[tex]\color{red}= 12 + 3 \\
\color{red}= 15 \: inches[/tex]
Let us check whether we have found out the correct measurement of length and width or not by checking whether they form the given perimeter :-
[tex] = 2(l + b) = 54[/tex]
[tex] = 2(12 + 15) = 54[/tex]
[tex] = 24 + 30 = 54[/tex]
[tex]54 = 54[/tex]
LHS = RHS , which means we have found out the correct measurement of the length and width of this rectangle .
Therefore , the length of this rectangle = 15 inches and the width of this rectangle = 12 inches .