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