The answer to the question I believe is 3.
It is a 30,60,90 triangle, so x = 4, and y = 2
I graphed the vertices and got a triangle but its very hard to solve its perimeter. Therefore, I identified right triangles to help me solve for the perimeter making each side the hypotenuse of each right triangle.
Pythagorean Theorem: a² + b² = c²
a = short leg ; b = long leg ; c = hypotenuse
P(0,0) ; R(-3,4)
a = 3 ; b = 4 ;
3² + 4² = c²
9 + 16 = c²
25 = c²
√25 = √c²
5 = c
P(0,0) ; Q(8,6)
a = 6 ; b = 8
6² + 8² = c²
36 + 64 = c²
100 = c²
√100 = √c²
10 = c
Q(8,6) ; R(-3,4)
a = 2 ; b = 11
2² + 11² = c²
4 + 121 = c²
125 = c²
√125 = √c²
11.18 = c
Perimeter = 5 + 10 + 11.18 = 26.18
