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the area of a square is given by the expression x^2-12x+36 square inches. find an expression that represents the length of one side of the square in inches

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rabinshrestha41

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, 
\(L= \sqrt{A}\)..........we get this by square rooting on both sides in the formula

\(L= \sqrt{ x^{2} -12x+36}\)

\(L= \sqrt{ (x)^{2} -2*x*6+ (6)^{2} }\)..............(a-b)²=a²-2ab+b²

\(L= \sqrt{ (x-6)^{2} }\)..................................(a-b)²=a²-2ab+b²

\(L=x-6\)...............................square cancels square root

So, the expression that represents the length of one side of square is x - 6 inches.

MrRoyal

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:

\(\mathbf{Area = x^2 -12x + 36}\)

Expand

\(\mathbf{Area = x^2 -6x - 6x + 36}\)

Factorize

\(\mathbf{Area = x(x -6) - 6(x - 6)}\)

Factor out x - 6

\(\mathbf{Area = (x -6) (x - 6)}\)

Express as squares

\(\mathbf{Area = (x -6)^2}\)

The length of a square is the square root of its area.

So, we have:

\(\mathbf{Length= \sqrt{(x -6)^2}}\)

\(\mathbf{Length= x -6}\)

Hence, the length of one side of the square is x - 6

Read more about squares at:

https://brainly.com/question/1658516

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