Answer:
Let the width of the rectangle be w.
Let the length of the rectangle be l.
★ If the length is 3 feet longer than the width, then the length can be written in terms of the width as:
Now, the formula for finding the perimeter is p = 2l + 2w.
Substituting the values in this formula -
[tex] \\ \implies \sf \: p = 2(w + 3) + 2w \\ \\ \\ \implies \sf \: p = 2w + 6 + 2w \\ \\ \\ \implies \sf \: p = 4w + 6 \\ [/tex]
Substituting P = 30 for p ( allows us to solve for p) -
[tex] \\ \implies \sf \: 30 = 4w + 6 \\ \\ \\ \implies \sf \: 30 - 6 = 4w + 6 - 6 \\ \\ \\ \implies \sf24 = 4w \\ \\ \\ \implies \sf \: w = \frac{24}{4} \\ \\ \\ \dag \: \large{ \underline{ \boxed{ \sf{ \: w = 6 \: cm}}}} \\ [/tex]
Substituting w = 6 for l in the equation l = w + 7 -
[tex] \\ \implies \sf \: l = 6 + 7 \\ \\ \\ \implies \sf \blue{l = 13 \: cm}[/tex]
