Respuesta :

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Answer:

[tex]4\sqrt{2}[/tex]

Step-by-step explanation:

distance formula:[tex]\sqrt{\left(x_2-x_1\right)^{2}+\left(y_2-y_1\right)^{2}}[/tex]

set square to be centered on the origin and find the distance between 2 of the connected points

[tex]\sqrt{\left(3-2\right)^{2}+\left(2-1\right)^{2}}[/tex]

= [tex]\sqrt{\left(1\right)^{2}+\left(1\right)^{2}}[/tex]

= [tex]\sqrt{2}[/tex]

multiply by 4 as it is a square and all of its sides are equal

[tex]4\sqrt{2}[/tex]

insert units

[tex]4\sqrt{2}\ \ meters[/tex]

The perimeter of the square is √32.

Given to us

  • the radius of the circle is 1 meter

What is the diagonal of the square inscribed in the circle?

As we can see in the figure AB is the diagonal of the square and diameter of the circle. therefore,

AB = Diagonal of the square = Diameter of circle = 2 x Radius = 2 meter

We know the diagonal of a square is equal to the product of √2 and the side of the square.

[tex]Diagonal = side \times {\sqrt2}[/tex]

Substitute the value,

[tex]2 = side \times {\sqrt2}\\\\side = \dfrac{2}{\sqrt2}\\\\side ={\sqrt2}[/tex]

What is the perimeter of the square?

The perimeter of the square is four times the side of the square.

[tex]Perimeter = 4\times (side)[/tex]

Substitute the value,

[tex]Perimeter = 4\times (\sqrt2)\\\\Perimeter = 4\sqrt2 = \sqrt{2\times 16} = \sqrt{32}[/tex]

Hence, the perimeter of the square is √32.

Learn more about Square:

https://brainly.com/question/11611396

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