Answer: The correct option is (D) 18 units.
Step-by-step explanation: We are given to find the perimeter of triangle ABC.
As shown in the attached figure below, triangle ABC is divided into two right-angled triangles ABD and ACD.
From the figure, we note that
AC = 8 units.
And the side lengths AB and BC are calculated using Pythagoras theorem of right-angled triangles as follows :
[tex]AB=\sqrt{AD^2+BD^2}=\sqrt{3^2+4^2}=\sqrt{25}=5~\textup{units},\\\\BC=\sqrt{CD^2+BD^2}=\sqrt{3^2+4^2}=\sqrt{25}=5~\textup{units}.[/tex]
We know that the perimeter of a triangle is equal to the sum of the lengths of the three sides.
Therefore, the required PERIMETER of ΔABC is given by
[tex]P=AB+BC+AC=5+5+8=18~\textup{units}.[/tex]
Thus, the perimeter of ΔABC is 18 units.
Option (D) is CORRECT.
