Question

In the equilateral triangle XYZ, X is located at (-5, -9) and Z is located at (1, -17). What is the perimeter of Triangle XYZ? a 30 units b 10 units c 25 units d 5 units

Answer 1

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

$P=XY+YZ+XZ$

$P=3XZ$

Find the distance XZ

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

X is located at (-5, -9) and Z is located at (1, -17)

substitute the values in the formula

$XZ=\sqrt{(-17+9)^{2}+(1+5)^{2}}$

$XZ=\sqrt{(-8)^{2}+(6)^{2}}$

$XZ=\sqrt{100}$

$XZ=10\ units$

Find the perimeter

$P=3(10)=30\ units$