Answer:
option c is correct.
side = z+9
Step-by-step explanation:
Area of a square(A) is given by:
[tex]A = s^2[/tex]
where,
s is the side of the square.
As per the statement:
A certain square has an area of [tex]z^2 + 18z + 81.[/tex]
⇒[tex]A = z^2 + 18z + 81[/tex]
Substitute in [1] we have;
[tex]z^2 + 18z + 81 = s^2[/tex]
Taking square root both sides we have;
[tex]\sqrt{z^2 + 18z + 81} =s[/tex]
Using identity rule:
[tex](a+b)^2 =a^2+2ab+b^2[/tex]
then;
[tex]\sqrt{z^2 + 2(1)(9)z + 9^2} =s[/tex]
⇒[tex]\sqrt{(z+9)^2} =s[/tex]
Simplify:
[tex]z+9 = s[/tex]
or
s = z+9
Therefore, a side of the square. is, z+9
