[tex]\huge\text{$(18x+15)$ units}[/tex]
Given the area, we need to find the side length. Let's start with the area equation for a square, where [tex]s[/tex] is the side length and [tex]A[/tex] is the area.
[tex]s^2=A[/tex]
Substitute in the known value.
[tex]s^2=324x^2+540x+225[/tex]
Now we need to factor the trinomial. The trinomial given for the area is a perfect square trinomial since [tex]324[/tex] ([tex]18^2[/tex]) and [tex]225[/tex] ([tex]15^2[/tex]) are both perfect squares.
We also know that [tex]a^2+2ab+b^2=(a+b)^2[/tex], which we can use to factor.
[tex]s^2=324x^2+540x+225\\s^2=(18x)^2+2(18x)(15)+15^2\\s^2=(18x+15)^2[/tex]
Now, take the square root of both sides to fully isolate [tex]s[/tex].
[tex]\sqrt{s^2}=\sqrt{(18x+15)^2}[/tex]
Keep in mind that the square root of any value squared is the original value.
[tex]s=\boxed{18x+15}[/tex]
