we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have a triangle
so
the polygon has three sides
Let
[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]
the perimeter is equal to
[tex]P=AB+BC+AC[/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 AB
[tex]A(-5,4)\\B(1,4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAB=6\ units[/tex]
Step 2
Find the distance BC
[tex]B(1,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]dBC=8.25\ units[/tex]
Step 3
Find the distance AC
[tex]A(-5,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{128}[/tex]
[tex]dAC=11.31\ units[/tex]
Step 4
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
substitutes the values
[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]
therefore
the answer is
[tex]25.6\ units[/tex]
