Question

What is the perimeter of ΔBDE?

Answer 1

a = √1² + 2²
a = √1 + 4
a = √5
a ≈ 2.23

b = 4

c = √3² + 2²
c = √9 + 4
c = √13
c ≈ 3.6

P = a + b + c
P = 2.23 + 4 + 3.6
P = 6.23 + 3.6
P = 9.83

Perimeter of ΔBDE = 9.83 units

Answer 2

9.84 units.

Explanation:

We will use distance formula to find the perimeter of the given triangle.

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\text{Distance between B and D}=√((2-1)^2+(4-2)^2)`

`\text{Distance between B and D}=√((1)^2+(2)^2)`

`\text{Distance between B and D}=√(1+4)`

`\text{Distance between B and D}=√(5)`

`\text{Distance between D and E}=√((5-2)^2+(2-4)^2)`

`\text{Distance between D and E}=√((3)^2+(-2)^2)`

`\text{Distance between D and E}=√(9+4)`

`\text{Distance between D and E}=√(13)`

We can see the distance between B and E is 4 units (5-1).

`\text{Perimeter of triangle BDE}=√(5)+√(13)+4`

`\text{Perimeter of triangle BDE}=9.841619252\approx 9.84`

Therefore, the perimeter of triangle BDE is 9.84 units.