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

Answer:

9.84 units.

Step-by-step explanation:

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

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

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

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

$\text{Distance between B and D}=\sqrt{1+4}$

$\text{Distance between B and D}=\sqrt{5}$

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

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

$\text{Distance between D and E}=\sqrt{9+4}$

$\text{Distance between D and E}=\sqrt{13}$

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

$\text{Perimeter of triangle BDE}=\sqrt{5}+\sqrt{13}+4$

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

Therefore, the perimeter of triangle BDE is 9.84 units.