Answer:
a) [tex]\displaystyle \sqrt{17} + \sqrt{26} + 5[/tex]
Step-by-step explanation:
To find the length of all three sides, you have to use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D[/tex]
D[2, 6], and B[−2, 3] → DB
[tex]\displaystyle \sqrt{[-2 - 2]^2 + [-6 + 3]^2} = \sqrt{[-4]^2 + [-3]^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
DB is 5 units long.
E[3, 2] and B[−2, 3] → EB
[tex]\displaystyle \sqrt{[-3 - 2]^2 + [-2 + 3]^2} = \sqrt{[-5]^2 + 1^2} = \sqrt{25 + 1} = \sqrt{26}[/tex]
EB is [tex]\displaystyle \sqrt{26}[/tex]units long.
E[3, 2] and D[2, 6] → ED
[tex]\displaystyle \sqrt{[-3 + 2]^2 + [-2 + 6]^2} = \sqrt{[-1]^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]
ED is [tex]\displaystyle \sqrt{17}[/tex]units long.
Altogether, you have the perimeter of [tex]\displaystyle \sqrt{17} + \sqrt{26} + 5[/tex]units.
I am joyous to assist you anytime.
* Since we are talking about distance, we ONLY want the NON-NEGATIVE roots.
