Answer
(3n+9)
Work Step by Step
Given the polynomial $(3n)^{2}$ + 54n + $(9)^{2}$
We see that the polynomial has the first and last term squared and the middle term is +2 times the first and last term.
Thus it follows the rule of $a^{2}$ + 2ab + $b^{2}$ = $(a+b)^{2}$ In this polynomial a= 3n and b=9
$(3n)^{2}$ + 2(3n)(9) + $(9)^{2}$ = $(3n+9)^{2}$
The formula for area of a square is $Length^{2}$ so the area is $(3n+9)^{2}$
T get the length we square root our area. $\sqrt (3n+9)^{2}$ = (3n+9)(3n+9). Thus the length is (3n+9)
