Keywords
triangle,perimeter,distance, length, side, points
we know that
The perimeter of a triangle is the sum of the three length side
To find the length side calculate the distance between two points
The formula to calculate the distance between to points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance ZY
[tex]Z(1,0)\\Y(3,1)[/tex]
substitute the values
[tex]d=\sqrt{(1-0)^{2}+(3-1)^{2}}[/tex]
[tex]dZY=\sqrt{5}\ units[/tex]
Step 2
Find the distance XY
[tex]X(-1,4)\\Y(3,1)[/tex]
substitute the values
[tex]d=\sqrt{(1-4)^{2}+(3+1)^{2}}[/tex]
[tex]dXY=\sqrt{25}=5\ units[/tex]
Step 3
Find the perimeter of the triangle
[tex]P=ZX+ZY+XY[/tex]
we have
[tex]dZX=2\sqrt{5}\ units[/tex]
[tex]dZY=\sqrt{5}\ units[/tex]
[tex]dXY=5\ units[/tex]
Substitute
[tex]P=(2\sqrt{5}+\sqrt{5}+5)\ units[/tex]
therefore
the answer is
[tex]P=(3\sqrt{5}+5)\ units[/tex]
