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Step-by-step explanation:

Let
y> the length of the rectangle
x> the width of the rectangle
P> perimeter of a rectangle

we know that
P=38 ft
[P]=2*[x+y]> 38=2*[x+y]> equation 1
y=5+x> equation 2
substitute 2 in 1
P=2*[x+(5+x)]> P=4x+10> the given equation
4x=38-10> 4x=28> x=7 ft
y=5+7> y=5+7> y=12 ft

the answer is
the width is 7 ft