Answer: The perimeter is about 20.26 units
Step-by-step explanation:
To calculate the distance between the points, we use the formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance
[tex]x_2\text{ and }x_1[/tex] are the coordinates of the points on x-axis
[tex]y_2\text{ and }y_1[/tex] are the coordinates of the points on y-axis
For the given points:
B(0,3), C(4,-1), E(2,-3) and F(-2,1)
- Calculating the distance BC:
[tex]x_2=4\\x_1=0\\y_2=-1\\y_1=3[/tex]
Putting values in above equation, we get:
[tex]BC=\sqrt{(4-(0))^2+(-1-3)^2}\\\\d=\sqrt{16+16}=5.66units[/tex]
- Calculating the distance CE:
[tex]x_2=2\\x_1=4\\y_2=-3\\y_1=-1[/tex]
Putting values in above equation, we get:
[tex]CE=\sqrt{(2-(4))^2+(-3-(-1))^2}\\\\d=\sqrt{36+4}=4.47units[/tex]
To calculate the perimeter of a rectangle, we use the equation:
[tex]Perimeter=2(l+b)[/tex] ....(1)
where,
l = length of the rectangle = BC = 5.66 units
b = breadth of the rectangle = CE = 4.47 units
Putting values in equation 1, we get:
[tex]Perimeter=2(5.66+4.47)\\\\Perimeter=20.26 units[/tex]
Hence, the perimeter is about 20.26 units
