Answer:
The perimeter of parallelogram WXYZ is 2√5 + 2√17 units or also known as about 12.72 units.
Step-by-step explanation:
In the diagram, we have a parallelogram. A parallelogram is a shape with two pairs of congruent sides. So, this means that we only need to find the measurement of two sides. From there, we are going to multiply those individual measurements by 2 because both has another side that is congruent to them. Lastly, we will add up all of the measurements to find the perimeter.
We can find the lengths by using the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]
Let's find the length of WX.
[tex]WX=\sqrt{(4-0)^2+(0-(-1))^2}[/tex]
[tex]WX=\sqrt{((4)^2+(1)^2)}[/tex]
[tex]WX=\sqrt{16+1}[/tex]
[tex]WX=\sqrt{17}[/tex]
Now, we multiply this number by 2 because ZY is congruent to this side.
√17 × 2 = 2√17
Now, let's find the length of WZ.
[tex]WZ=\sqrt{(0-(-1))^2+(-1-(-3))^2}[/tex]
[tex]WZ=\sqrt{(1)^2+(2)^2}[/tex]
[tex]WZ=\sqrt{1+4}[/tex]
[tex]WZ=\sqrt{5}[/tex]
Now, we multiply this number by 2 because XY is congruent to this side.
√5 × 2 = 2√5
Now, we add these numbers together to get the perimeter.
2√5 + 2√17 = 12.72
The required perimeter of parallelogram WXYZ is [tex]2\times \sqrt5 + 2\times \sqrt17 \ units[/tex].
We have to determine, The perimeter of parallelogram WXYZ.
According to the question,
A parallelogram is a shape with two pairs of congruent sides. So, this means need to find the measurement of two sides.
From there, multiply those individual measurements by 2 because both has another side that is congruent to them. Lastly, add up all of the measurements to find the perimeter.
To find the lengths by using the distance formula,
[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WX = \sqrt{(4-0)^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{16+1} \\\\WX = \sqrt{17}[/tex]
Then, multiply this number by 2 because ZY is congruent to this side.
[tex]\sqrt{17} \times 2= 2 \sqrt{17}[/tex]
Now, let's find the length of WZ by using distance formula,
[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WZ = \sqrt{((-1)-(-3))^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{4+1} \\\\WX = \sqrt{5}[/tex]
Now, multiply this number by 2 because XY is congruent to this side.
[tex]=\sqrt{5} \times 2= 2\sqrt{5}[/tex]
Therefore, adding these numbers together to get the perimeter of parallelogram WXYZ,
Perimeter of parallelogram WXYZ [tex]=2\times \sqrt5 + 2\times \sqrt17 \ units[/tex]
Hence, The required perimeter of parallelogram WXYZ is [tex]2\times \sqrt5 + 2\times \sqrt17 \ units[/tex].
To know more about Parallelogram click the link given below.
https://brainly.com/question/14592910
