Final answer:
To find the length of side AB, we use the fact that the perpendicular bisector of AB intersects BC at point D and the perimeters of the two triangles. By setting up and solving an equation, we find that the length of AB is 12cm.
Step-by-step explanation:
To find the length of side AB, we need to use the information given:
The perpendicular bisector of side AB intersects side BC at point D.
The perimeter of triangle ABC is 12cm larger than the perimeter of triangle ACD.
Let's denote the length of AB as x. Since the perpendicular bisector intersects BC at point D, we can conclude that BD = DC.
Therefore, the perimeter of triangle ABC is 2x + BC.
The perimeter of triangle ACD is x + AD + AC.
Since the perimeter of triangle ABC is 12cm larger than the perimeter of triangle ACD, we can set up the equation:
2x + BC = x + AD + AC + 12
Simplifying the equation, we get:
x = AD + AC + 12 - BC
Since AD + AC is the perimeter of triangle ACD, which is equal to BC, we can substitute BC for AD + AC:
x = BC + 12 - BC
x = 12
Therefore, the length of side AB is 12cm.