Question

What is the perimeter of rhombus WXYZ?

StartRoot 13 EndRoot units
12 units
StartRoot 13 EndRoot units
20 units

Answer 1

C) 4 \sqrt{13}

Explanation:

Answer 2

The perimeter of rhombus WXYZ is
`4 √(13)`

Explanation:

Step 1 :Finding length of XY

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= 5

`x_2`=3

`y_1`= -1

`y_2`=2

XY =
`√((3-5)^2 +(2 -(-1))^2)`

XY =
`√((3-5)^2 +(2 +1))^2)`

XY =
`√((-2)^2 +(3))^2)`

XY =
`√(4 +9)`

XY =
`√((13))`

Step 2 :Finding length of YZ

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= 3

`x_2`=5

`y_1`= 2

`y_2`=5

YZ =
`√((5-3)^2 +(5-2)^2)`

YZ =
`√((2)^2 +(3)^2)`

YZ =
`√(4 +9)`

YZ =
`√((13))`

Step 3 : :Finding length of ZW

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= 5

`x_2`=7

`y_1`= 5

`y_2`=2

ZW =
`√((7-5)^2 +(5-2)^2)`

ZW =
`√((2)^2 +(3)^2)`

ZW =
`√(4 +9)`

ZW =
`√((13))`

Step 4 :Finding length of WX

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= 7

`x_2`=5

`y_1`= 2

`y_2`= -1

WX =
`√((7-5)^2 +((-1)-2)^2)`

WX =
`√((2)^2 +(-3)^2)`

WX =
`√(4 +9)`

WX =
`√((13))`

Step 5: finding the perimeter of the rhombus

Perimeter= 4 X side

=>
`4 * √(13)`

=>
`4 √(13)`