Question

The area of a square is defined by, A(x) = x 2 - 12x + 36. What is the length of a side of the square?

Answer 1

A(x) = x 2 - 12x + 36
A(x) = (x -6)^2

answer: length of a side of the square = x - 6

Answer 2

Answer: The required length of a side of the square is (x - 6) units.

Step-by-step explanation:  Given that the area of a square is as follows :

$A(x)=x^2-12x+36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the length of a side of the square.

We know that

all the sides of a square have equal length l, and its area is given by

$A=l^2.$

From expression (i), we have

$A(x)\\\\=x^2-12x+36\\\\=x^2-2\times x\times 6+6^2\\\\=(x-6)^2.$

Therefore, the required length of a side of the square is (x - 6) units.