Answer:
Option a. 30 units
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides
so
XY=YZ=XZ
The perimeter of triangle XYZ is equal to
[tex]P=XY+YZ+XZ[/tex]
[tex]P=3XZ[/tex]
Find the distance XZ
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
X is located at (-5, -9) and Z is located at (1, -17)
substitute the values in the formula
[tex]XZ=\sqrt{(-17+9)^{2}+(1+5)^{2}}[/tex]
[tex]XZ=\sqrt{(-8)^{2}+(6)^{2}}[/tex]
[tex]XZ=\sqrt{100}[/tex]
[tex]XZ=10\ units[/tex]
Find the perimeter
[tex]P=3(10)=30\ units[/tex]
