The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.

Answer:Hence, AB=12.Step-by-step explanation:We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.this means that side AE=BE.Also we could clear;ly observe thatΔBED≅ΔAED( since AE=BE, side ED common, ∠BED=∠AED so by SAS congruency the two triangles are congruent)Now we are given that:the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.i.e. AB+AC+BC=AC+AD+CD+12AB+BC=AD+CD+12as AD=BDthis means that AD+CD=BD+CD=BCAB+BC=BC+12AB=12Hence AB=12