we know that
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself
so
[tex](a^{2} +2ab+b^{2})=(a+b)^{2}[/tex]
in this problem we have
[tex]9x^{2} +24x+16[/tex]
both [tex]9x^{2}[/tex] and [tex]16[/tex] are perfect squares
hence
[tex]9x^{2} +24x+16=(3x+4)^{2}[/tex]
[tex]Length=(3x+4)\ units[/tex]
[tex]Width=(3x+4)\ units[/tex]
therefore
the answer is
both: 3x + 4 units
