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 = A ..........we get this by square rooting on both sides in the formula
L = x 2 − 12 x + 36
L = ( x ) 2 − 2 ∗ x ∗ 6 + ( 6 ) 2 ..............(a-b)²=a²-2ab+b²
L = ( 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.
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:
Area = x 2 − 12x + 36
Expand
Area = x 2 − 6x − 6x + 36
Factorize
Area = x ( x − 6 ) − 6 ( x − 6 )
Factor out x - 6
Area = ( x − 6 ) ( x − 6 )
Express as squares
Area = ( x − 6 ) 2
The **length **of a **square **is the **square root **of its area .
So, we have:
Length = ( x − 6 ) 2
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
The expression that represents the length of one side of the square is x − 6 inches, derived from factoring the quadratic expression given for the area. By recognizing the area formula L 2 = A and factoring the quadratic as ( x − 6 ) 2 , we find that the side length is the square root of this expression. Taking the positive root gives us the final expression for the length.
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