Answer:
Option A. [tex]21.21\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of a triangle is equal to the sum of its three side lengths
so
[tex]P=EF+FG+EG[/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]E(5,4),F(9,1),G(5,-5)[/tex]
step 1
Find the distance EF
[tex]E(5,4),F(9,1)[/tex]
substitute in the formula
[tex]EF=\sqrt{(1-4)^{2}+(9-5)^{2}}[/tex]
[tex]EF=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
[tex]EF=\sqrt{25}[/tex]
[tex]EF=5\ units[/tex]
step 2
Find the distance FG
[tex]F(9,1),G(5,-5)[/tex]
substitute in the formula
[tex]FG=\sqrt{(-5-1)^{2}+(5-9)^{2}}[/tex]
[tex]FG=\sqrt{(-6)^{2}+(-4)^{2}}[/tex]
[tex]FG=\sqrt{52}[/tex]
[tex]FG=7.21\ units[/tex]
step 3
Find the distance EG
[tex]E(5,4),G(5,-5)[/tex]
substitute in the formula
[tex]EG=\sqrt{(-5-4)^{2}+(5-5)^{2}}[/tex]
[tex]EG=\sqrt{(-9)^{2}+(0)^{2}}[/tex]
[tex]EG=\sqrt{81}[/tex]
[tex]EG=9\ units[/tex]
step 4
Find the perimeter
[tex]P=EF+FG+EG[/tex]
[tex]P=5+7.21+9=21.21\ units[/tex]
