Answer: The correct option is
(A) 19.7 units.
Step-by-step explanation: We are given to find the perimeter of triangle PQR and round the answer to the nearest tenth.
From the figure, we note that the co-ordinates of the vertices of triangle PQR are P(-2, 1), Q(6, 1) and R(4, -3).
We know that the perimeter of a triangle is equal to the sum of the lengths of its three sides.
The lengths of the sides PQ, QR and PR can be calculated using distance formula as follows :
[tex]PQ=\sqrt{(6+2)^2+(1-1)^2}=\sqrt{8^2}=8,\\\\QR=\sqrt{(4-6)^2+(-3-1)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt5=4.4721,\\\\PR=\sqrt{(4+2)^2+(-3-1)^2}=\sqrt{36+16}=\sqrt{52}=2\sqrt{13}=7.2111.[/tex]
Therefore, the perimeter of triangle PQR is given by
[tex]p=PQ+QR+PR=8+5.4721+7.2111=19.6832.[/tex]
Rounding to the nearest tenth, we get
p = 19.7 units.
Thus, the required perimeter of triangle PQR is 19.7 units.
Option (A) is CORRECT.
