given triangle ACD is isosceles with angle D as the vertex angle and B is the midpoint of segment AC. AB=x+5 and BC=2x-3 and CD=2x+6. what is the perimeter of triangle ACD?

Question

given triangle ACD is isosceles with angle D as the  vertex angle. B is the midpoint of segment AC. AB=xd+5 and BC=2x-3 and CD=2x+6.  What is the perimeter of triangle ACD?

Answer 1

If B is the midpoint of AC, then AB=BC, so x+5=2x-3, so subtracting from each side, 5=x-3 and adding 3 to each side  8=x, so x=8 and AB=BC=13, making AC=26. The two sides of the triangle AD and DC are equal because it's isosceles so AD=CD=2x+6=22, because x=8 and the perimeter=AD+CD+AC=22+22+26=70.