Question

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

Option 1: 6 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 12 cm

Answer 1

To find AB, we need to use the concept of the perpendicular bisector. The perpendicular bisector of side AB passes through the midpoint of AB at a right angle. This means that point D, the intersection of the perpendicular bisector and side BC, is equidistant from A and B. So, AD = DB. Since the perimeter of ABC is 12 cm larger than the perimeter of AC, we can set up the equation AB + BC + AC = AC + BC + AC + 12. Simplifying this equation, we get AB = 12 cm.

Step-by-step explanation:

The perpendicular bisector of side AB of triangle ABC intersects side BC at point D. To find AB, we need to use the concept of the perpendicular bisector. The perpendicular bisector of side AB passes through the midpoint of AB at a right angle. This means that point D, the intersection of the perpendicular bisector and side BC, is equidistant from A and B. So, AD = DB. Since the perimeter of ABC is 12 cm larger than the perimeter of AC, we can set up the equation AB + BC + AC = AC + BC + AC + 12. Simplifying this equation, we get AB = 12 cm.