We will represent the length of the rectangle as [tex] l [/tex] and the width as [tex] w [/tex].
From this problem, we can say [tex] l = w + 5 [/tex]. We can also deduct an equation from the second sentence:
[tex] 2l + 2w = 82 [/tex]
[tex] 2(w + 5) + 2w = 82 [/tex] (from substitution)
[tex] 2w + 10 + 2w = 82 [/tex]
[tex] 4w = 72 [/tex]
[tex] \boxed{w = 18} [/tex]
Using this value for [tex] w [/tex], we can find [tex] l [/tex]:
[tex] l = 18 + 5 [/tex]
[tex] \boxed{l = 23} [/tex]
The length of the rectangle is 23 cm and the width of the rectangle is 18 cm.
