Answer:
The approximate perimeter of the triangle is 10.5 units
Step-by-step explanation:
we know that
The perimeter of triangle is equal to the sum of its three length sides
so
[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]
step 1
Find the distance XY
we have
x [-6,-4], y [-10,-2]
substitute in the formula
[tex]d=\sqrt{(-2+4)^{2}+(-10+6)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-4)^{2}}[/tex]
[tex]d_X_Y=\sqrt{20}\ units[/tex]
step 2
Find the distance YZ
we have
y [-10,-2], z [-6,-2]
substitute in the formula
[tex]d=\sqrt{(-2+2)^{2}+(-6+10)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d_Y_Z=4\ units[/tex]
step 3
Find the distance XZ
we have
x [-6,-4], z [-6,-2]
substitute in the formula
[tex]d=\sqrt{(-2+4)^{2}+(-6+6)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(0)^{2}}[/tex]
[tex]d_X_Z=2\ units[/tex]
step 4
Find the perimeter
[tex]P=XY+YZ+XZ[/tex]
substitute
[tex]P=\sqrt{20}+4+2=(\sqrt{20}+6)\ units[/tex] ----> exact value
[tex]P=\sqrt{20}+6=10.5\ units[/tex] ----> approximate value
