Question

Can someone please help me! Big ideas 8.4 number 20

Answer 1

Answer: The perimeter is about 20.26 units

Step-by-step explanation:

To calculate the distance between the points, we use the formula:

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

where,

d = distance

$x_2\text{ and }x_1$ are the coordinates of the points on x-axis

$y_2\text{ and }y_1$ 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:

$x_2=4\\x_1=0\\y_2=-1\\y_1=3$

Putting values in above equation, we get:

$BC=\sqrt{(4-(0))^2+(-1-3)^2}\\\\d=\sqrt{16+16}=5.66units$

• Calculating the distance CE:

$x_2=2\\x_1=4\\y_2=-3\\y_1=-1$

Putting values in above equation, we get:

$CE=\sqrt{(2-(4))^2+(-3-(-1))^2}\\\\d=\sqrt{36+4}=4.47units$

To calculate the perimeter of a rectangle, we use the equation:

$Perimeter=2(l+b)$ ....(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:

$Perimeter=2(5.66+4.47)\\\\Perimeter=20.26 units$

Hence, the perimeter is about 20.26 units