Answer :
the area of a square is A=L² where, L is the length of the square and A is the area of the square.
So,
[tex]L= \sqrt{A} [/tex]..........we get this by square rooting on both sides in the formula
[tex]L= \sqrt{ x^{2} -12x+36} [/tex]
[tex]L= \sqrt{ (x)^{2} -2*x*6+ (6)^{2} } [/tex]..............(a-b)²=a²-2ab+b²
[tex]L= \sqrt{ (x-6)^{2} } [/tex]..................................(a-b)²=a²-2ab+b²
[tex]L=x-6[/tex]...............................square cancels square root
So, the expression that represents the length of one side of square is x - 6 inches.
So,
[tex]L= \sqrt{A} [/tex]..........we get this by square rooting on both sides in the formula
[tex]L= \sqrt{ x^{2} -12x+36} [/tex]
[tex]L= \sqrt{ (x)^{2} -2*x*6+ (6)^{2} } [/tex]..............(a-b)²=a²-2ab+b²
[tex]L= \sqrt{ (x-6)^{2} } [/tex]..................................(a-b)²=a²-2ab+b²
[tex]L=x-6[/tex]...............................square cancels square root
So, the expression that represents the length of one side of square is x - 6 inches.
The area of a square is the products of its dimensions.
The length of one side of the square is x - 6
The area is given as:
[tex]\mathbf{Area = x^2 -12x + 36}[/tex]
Expand
[tex]\mathbf{Area = x^2 -6x - 6x + 36}[/tex]
Factorize
[tex]\mathbf{Area = x(x -6) - 6(x - 6)}[/tex]
Factor out x - 6
[tex]\mathbf{Area = (x -6) (x - 6)}[/tex]
Express as squares
[tex]\mathbf{Area = (x -6)^2}[/tex]
The length of a square is the square root of its area.
So, we have:
[tex]\mathbf{Length= \sqrt{(x -6)^2}}[/tex]
[tex]\mathbf{Length= x -6}[/tex]
Hence, the length of one side of the square is x - 6
Read more about squares at:
https://brainly.com/question/1658516
