In an isosceles triangle ABC with base AC, a median BM equal to 8cm is drawn.

In an isosceles triangle ABC with base AC, a median BM equal to 8cm is drawn. What is the perimeter of triangle ABC if BC = 10cm.

The median BM of the isosceles triangle ABC is also the height of this triangle, then the triangles ABM and BCM are rectangular.

By the Pythagorean theorem, in the right-angled triangle of the BCM, we determine the length of the CM leg.

CM ^ 2 = BC ^ 2 – BM ^ 2 = 100 – 64 = 36.

CM = 6 cm.

Since BM is the median, then AM = CM, and therefore AC = CM * 2 = 6 * 2 = 12 cm.

AB = BC = 10 cm, since they are the lateral sides of an isosceles triangle.

Then the perimeter of the triangle ABC is equal to: Ravs = 2 * AB + AC = 2 * 10 + 12 = 32 cm.

Answer: The perimeter of triangle ABC is 32 cm.