if the original segment, was 20ft long
then you cut it in two
say
a b
-------------------------------------------
^
cut it here
so, the shorter side is "a"
and the longer is "b"
notice, originally it was a 20ft long
so, whatever the pieces are, must
add up to 20
thus
a + b = 20
now
5 times the smaller
5*a or 5a
equals 2 more than the longer
b + 2
so 5a = b +2
[tex]\bf \begin{cases}
a+b=20\implies b=\boxed{20-a}\\
5a=b+2\\
---------\\
5a=\boxed{20-a}+2
\end{cases}[/tex]
solve for "a", to get the shorter one
what's the longer one? well, 20 - a
