Answer:
24.98 units
Step-by-step explanation:
The picture of the question in the attached figure
we have the coordinates
P(1,-6),D(4,3),O(7,-6)
The perimeter of triangle OPD is equal to
[tex]P=OP+PD+OD[/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 OP
we have
O(7,-6),P(1,-6)
substitute in the formula
[tex]d=\sqrt{(-6+6)^{2}+(1-7)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-6)^{2}}[/tex]
[tex]d_O_P=6\ units[/tex]
step 2
Find the distance PD
we have
P(1,-6),D(4,3)
substitute in the formula
[tex]d=\sqrt{(3+6)^{2}+(4-1)^{2}}[/tex]
[tex]d=\sqrt{(9)^{2}+(3)^{2}}[/tex]
[tex]d_P_D=\sqrt{90}\ units[/tex]
step 3
Find the distance OD
we have
O(7,-6),D(4,3)
substitute in the formula
[tex]d=\sqrt{(3+6)^{2}+(4-7)^{2}}[/tex]
[tex]d=\sqrt{(9)^{2}+(-3)^{2}}[/tex]
[tex]d_O_D=\sqrt{90}\ units[/tex]
step 4
Find the perimeter
[tex]P=6+\sqrt{90}+\sqrt{90}[/tex]
[tex]P=6+9.49+9.49=24.98\ units[/tex]
