Question

What is the perimeter of rhombus WXYZ?

Answer 1

Answer:

The perimeter of rhombus WXYZ is $4 \sqrt{13}$

Step-by-step explanation:

Step 1 :Finding length  of  XY

Distance formula  = $\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$

here

$x_1$= 5

$x_2$=3

$y_1$= -1

$y_2$=2

XY  = $\sqrt{(3-5)^2 +(2 -(-1))^2}$

XY  = $\sqrt{(3-5)^2 +(2 +1))^2}$

XY  = $\sqrt{(-2)^2 +(3))^2}$

XY  = $\sqrt{4 +9}$

XY  = $\sqrt{(13)}$

Step 2 :Finding length  of  YZ

Distance formula  = $\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$

here

$x_1$= 3

$x_2$=5

$y_1$= 2

$y_2$=5

YZ  = $\sqrt{(5-3)^2 +(5-2)^2}$

YZ = $\sqrt{(2)^2 +(3)^2}$

YZ = $\sqrt{4 +9}$

YZ  = $\sqrt{(13)}$

Step 3 : :Finding length  of  ZW

Distance formula  = $\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$

here

$x_1$= 5

$x_2$=7

$y_1$= 5

$y_2$=2

ZW = $\sqrt{(7-5)^2 +(5-2)^2}$

ZW  = $\sqrt{(2)^2 +(3)^2}$

ZW  = $\sqrt{4 +9}$

ZW = $\sqrt{(13)}$

Step 4 :Finding length  of  WX

Distance formula  = $\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$

here

$x_1$= 7

$x_2$=5

$y_1$= 2

$y_2$= -1

WX = $\sqrt{(7-5)^2 +((-1)-2)^2}$

WX  = $\sqrt{(2)^2 +(-3)^2}$

WX  = $\sqrt{4 +9}$

WX = $\sqrt{(13)}$

Step 5: finding the perimeter of the rhombus

Perimeter= 4 X side

=> $4 \times \sqrt{13}$

=> $4 \sqrt{13}$

Answer 2

Answer:

C) 4 \sqrt{13}

Step-by-step explanation: