Answer :

For this case, the first thing we must do is define the formula of distance between points.

We have then:

[tex] d = \sqrt{(x2-x1)^2 + (y2-y1)^2} [/tex]

From here, we look for the distance between two points of rhombus.

[tex] YZ = \sqrt{(5-3)^2 + (5-2)^2}

YZ = \sqrt{2^2 + 3^2}

YZ = \sqrt{4 + 9}

YZ = \sqrt{13} [/tex]

Then, since all sides have the same length, then the perimeter is given by:

[tex] P = 4YZ [/tex]

Substituting we have:

[tex] P = 4\sqrt{13} [/tex]

Answer:

The perimeter of the rhombus is:

[tex] P = 4\sqrt{13} [/tex]

option 3

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Rewritten by : Barada

Answer:

To find the perimeter of a rhombus, use the distance equation, [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}^[/tex]. This gives us c) 4√13 as the perimeter.

Step-by-step explanation:

The distance equation, [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}^[/tex], can be used to find the distance between two points in the coordinate grid. Let's start by finding the distance between points Y and Z (I will assign Y to point 1 and Z to point 2).

[tex]d=\sqrt{(3-5)^2+(2-5)^2} \\d=\sqrt{(-2)^2+(-3)^2} \\d=\sqrt{13}[/tex]

So, the distance of line YZ is √13 units. Notice that the other three lines also have a vertical distance of 3 and a horizontal distance of 2, so they are all the same length.

Therefore, to find the total perimeter, multiply the length of one side by 4. √13 x 4 = 4√13, so that is our final answer.