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The area of a square rug can be represented by the expression 100x^2+60x+9. Write an expression to represent the length of each side of the rug.

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ANSWER:

square root of ( 100x^2 + 60x + 9 )

An expression to represent the length of each side of the rug is:
square root of ( 100x^2 + 60x + 9 )

STEP-BY-STEP EXPLANATION:

Let's establish that the area of a square is the length of one of its sides squared.

Area of square = Side^2

THEREFORE:

To find the length of each side of the square, we will make side the subject in the formula as displayed below.

Area of square = Side^2

Side^2 = Area of square

Side = square root of ( area of square )

From this, we will substitute the given expression for the area of the square rug to obtain the expression for the length of each side of the rug.

Side = square root of ( 100x^2 + 60x + 9 )

Answer : The expression to represent the length of each side of the rug is, [tex]Side=10x+3[/tex]

Step-by-step explanation :

As we know that the formula of area of square is:

Area of square = (Side)²

Given:

Area of square = [tex]100x^2+60x+9[/tex]

As,

Area of square = (Side)²

So,

[tex]100x^2+60x+9=(Side)^2[/tex]

[tex]\sqrt{100x^2+60x+9}=Side[/tex]

[tex]\sqrt{100x^2+30x+30x+9}=Side[/tex]

[tex]\sqrt{10x(10x+3)+3(10x+3)}=Side[/tex]

[tex]\sqrt{(10x+3)(10x+3)}=Side[/tex]

[tex]\sqrt{(10x+3)^2}=Side[/tex]

[tex](10x+3)=Side[/tex]

or,

[tex]Side=10x+3[/tex]

Thus, the expression to represent the length of each side of the rug is, [tex]Side=10x+3[/tex]

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