In an isosceles triangle ABC, a height BD of 8cm is drawn to the base of AC

In an isosceles triangle ABC, a height BD of 8cm is drawn to the base of AC. Find the perimeter of triangles BDC if the perimeter of triangle ABC is 38cm.

Let’s denote the lateral sides of the triangle through X cm, and the base of the AC through 2 * Y cm.

Since the height BD in an isosceles triangle is also its median, then AD = CD = AC / 2 = 2 * Y / 2 = Y cm.

The perimeter of the triangle ABC is then equal to: P = 2 * X + 2 * Y = 38 cm.

Then X + Y = 19 cm.

X + Y = AB + AD = BC + CD.

Then the perimeter of the triangle ВDC = (ВС + СD) + ВD = 19 + 8 = 27 cm.

Answer: The perimeter of the BDC triangle is 27 cm.