The length of side AB is 24 cm.
Let the length of the sides of the triangle ABC be AB=x, AC=y and CB=z.
Since the perpendicular bisector of side AB of Δ ABC intersects side BC at point D, we know that AD=BD=x/2.
We are also given that the perimeter of Δ ABC is 12 cm larger than the perimeter of Δ ACD. This means that:
x+y+z = (x/2)+y+z+12
Simplifying the equation, we get:
x/2 = 12
Solving for x, we find:
x = 24
Therefore, the length of side AB is 24 cm.
Question
The perpendicular bisector of side overline AB of △ ABC intersects side overline BC at point D. Find AB if the perimeter of △ ABC is 12 cm larger than the perimeter of △ ACD. AB=□ cm