Here is a square inscribed in a circle with radius 1 meter. What is the perimeter of
the square? Explain or show your reasoning

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

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]

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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