# In an isosceles triangle ABC with base AC and height BD, find the length of the sides if AD = 3 cm

June 26, 2021 | education

| **In an isosceles triangle ABC with base AC and height BD, find the length of the sides if AD = 3 cm and perimeter = 20 cm**

The height BD of an isosceles triangle ABC is also the median of the triangle, then CD = AD = 3 cm, and then AC = AD + CD = 3 + 3 = 6 cm.

In an isosceles triangle, the lengths of the sides are equal, AB = BC. Let AB = BC = X cm.

Then the perimeter of the triangle ABC is equal to: Ravs = (X + X + 6) = 20.

2 * X = 20 – 6 = 14.

X = AB = BC = 14/2 = 7 cm.

Answer: The lengths of the sides of the triangle are 7 cm, 7 cm, 6 cm.