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

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* x* 6+6^2\\\\=(x-6)^2.`

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