The perimeter of the triangle is determined as: 33 units.
What is the Perimeter of a Triangle?
Perimeter of a triangle = sum of all its three side lengths.
What is the Angle Bisector Theorem?
If an angle bisector intersects the opposite side of a triangle, according to angle-bisector theorem, it divides the opposite side into two segments that are proportional to the two other sides.
The diagram for the triangle is given in the diagram below. Thus:
AB/AD = CB/CD ((angle bisector theorem).
Substitute
(x + 2)/6 = x/5
Cross multiply
5(x + 2) = 6x
5x + 10 = 6x
10 = 6x - 5x
10 = x
x = 10
Perimeter of Triangle = x + 2 + x + 5 + 6
Plug in the value of x
Perimeter of Triangle = 10 + 2 + 10 + 5 + 6
Perimeter of Triangle = 33 units.
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