Question

Find the perimeter of △CDE. Round your answer to the nearest hundredth. The perimeter is about units.

C(4,-1)
D(4,-5)
E(2,-3)

Answer 1

The perimeter of triangle CDE is found by calculating the lengths of its sides using the distance formula and adding them together. After calculating, the perimeter is approximately 9.66 units when rounded to the nearest hundredth.

Step-by-step explanation:

To find the perimeter of triangle CDE, we need to calculate the lengths of the sides of the triangle using the coordinates given for each vertex. The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be found using the distance formula: √((x2-x1)² + (y2-y1)²).

Let's calculate the lengths of the sides of triangle CDE:

• CD = √((4-4)² + (-5+1)²) = √(0 + (-4)²) = √16 = 4 units
• DE = √((2-4)² + (-3+5)²) = √((-2)² + (2)²) = √(4 + 4) = √8 ≈ 2.83 units
• CE = √((2-4)² + (-3+1)²) = √((-2)² + (-2)²) = √(4 + 4) = √8 ≈ 2.83 units

To find the perimeter, add the lengths of all three sides together:

P = CD + DE + CE ≈ 4 + 2.83 + 2.83 ≈ 9.66 units

Round the answer to the nearest hundredth to get the perimeter of the triangle.

Therefore, the perimeter of triangle CDE is approximately 9.66 units.

Answer 2

Answer:
`9.66\ units`

Step-by-step explanation:

The triangle CDE is shown in the image attached.

The formula for calculate the distance between two points is:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Then, we can calculate the lenght of each side of the triangle:

`d_(CD)=√((4-4)^2+(-5-(-1))^2)=4\ units\\\\d_(DE)=√((4-2)^2+(-5-(-3))^2)=2.828\ units\\\\d_(CE)=√((2-4)^2+(-3-(-1))^2)=2.828\ units`

Therefore, the perimeter is:

`P=4\ units+ 2.828\ units+2.828\ units=9.66\ units`