Answer :
EXPLANATION:
We are given the following details:
A square and a regular octagon have the same perimeter. However the sides are not given. Let us assign a variable to the sides of the octagon. One side of the octagon would be represented by letter x.
Note that it is a regular octagon which means all eight sides have the same length. Next we are told that one side of the square is 7 feet longer than one side of the octagon. This means one side of the square would be 7 + x. Note that a square too has all four sides with equal length.
Therefore we would hav e the following;
[tex]\begin{gathered} Octagon=x \\ Square=7+x \end{gathered}[/tex]Next we are told the two figures have the same perimeter.
The perimeter of an octagon is;
[tex]\begin{gathered} Octagon: \\ Perimeter=8x \\ Where: \\ x=length\text{ of one side} \end{gathered}[/tex]For a square we have;
[tex]\begin{gathered} Square: \\ Perimeter=4x \\ Where: \\ x=length\text{ of one side} \end{gathered}[/tex]Note however that the length of the square in this instance is (7 + x), hence we can re-write this equation as;
[tex]\begin{gathered} Square: \\ Perimeter=4\left(7+x\right) \end{gathered}[/tex]Since the perimeters for both are equal, we can equate both equations and we'll have;
[tex]8x=4\left(7+x\right)[/tex]We can now solve for the variable x;
[tex]8x=4\left(7+x\right)[/tex][tex]8x=28+4x[/tex]Combine like terms;
[tex]8x-4x=28[/tex][tex]4x=28[/tex]Divide both sides by 4;
[tex]\begin{gathered} \frac{4x}{4}=\frac{28}{4} \\ x=7 \end{gathered}[/tex]This means the length of a side of the octagon is 7 feet, while the length of a side of the square is 14 feet (7 + 7).
ANSWER:
[tex]\begin{gathered} Octagon=7ft \\ Square=14ft \end{gathered}[/tex]