Answer
The longer length of the wire is $19$ ft and the shorter length of the wire is $12$ ft.
Work Step by Step
Let $x = $ the longer length of the wire
$(x) + (x - 7) = 31$
$2x - 7 = 31$
$2x = 38$
$x = \frac{38}{2}$
$x = 19$ ft
Let $y = $ the shorter length of the wire
$y = (x - 7)$
$y = 19 - 7$
$y = 12$ ft