Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 50

A wire 12 ft long is cut into two pieces. Each piece is bent into the shape of a square. The perimeter of the larger square is twice the perimeter of the smaller square. Find the perimeter of the larger square.

If we let $x$ and $y$ be the perimeter of the smaller and larger square respectively, then we have

$x+y = 12 \qquad$ Equation 1

And

$y = 2x \qquad$ Equation 2

By substituting equation 1 to equation 2, we get


$
\begin{equation}
\begin{aligned}

x+ (2x) =& 12
\\
3x =& 12
\\
x =& 4

\end{aligned}
\end{equation}
$


Then, by applying back substitution,


$
\begin{equation}
\begin{aligned}

y =& 2x
\\
y =& 2(4)
\\
y =& 8

\end{aligned}
\end{equation}
$


Thus, the perimeter of the larger square is 8 ft.