In an isosceles triangle ABC with the base of BC, the median AM is drawn.

In an isosceles triangle ABC with the base of BC, the median AM is drawn. ABC perimeter = 40cm, and ABM perimeter = 34cm. Find the length of the median.

The perimeter of the isosceles triangle ABC:
Pabc = 2AB + BC = 40 cm.
Perimeter of triangle ABM:
Pabm = AB + BC / 2 + AM = 34 cm – since AM is the median;
AB + BC / 2 = Pabc / 2 = 40/2 = 20 cm.
Whence AM = Pabm – 20 = 34 – 20 = 14 cm.
Answer: The median length AM of triangle ABC is 14 cm.