Answer:
The perimeter is [tex]P=(15+\sqrt{65})\ units[/tex] or [tex]P=23.06\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of triangle XYZ is equal to the sum of its length sides
[tex]P=XY+YZ+XZ[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]X(0,2),Y(3,-2),Z(-7,-2)[/tex]
step 1
Find the distance XY
[tex]X(0,2),Y(3,-2)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(-2-2)^{2}+(3-0)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dXY=5\ units[/tex]
step 2
Find the distance YZ
[tex]Y(3,-2),Z(-7,-2)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(-2+2)^{2}+(-7-3)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-10)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]dYZ=10\ units[/tex]
step 3
Find the distance XZ
[tex]X(0,2),Z(-7,-2)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(-2-2)^{2}+(-7-0)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-7)^{2}}[/tex]
[tex]dXZ=\sqrt{65}\ units[/tex]
step 4
Find the perimeter
[tex]P=XY+YZ+XZ[/tex]
substitute
[tex]P=5+10+\sqrt{65}[/tex]
[tex]P=(15+\sqrt{65})\ units[/tex] ----> exact value
[tex]P=(15+8.06)=23.06\ units[/tex] -----> approximate value
