In an isosceles triangle ABC, the segment BD is the median drawn to the base

In an isosceles triangle ABC, the segment BD is the median drawn to the base. Find the perimeter of triangle BDC if the perimeter of triangle ABC is 12cm, BD = 5cm.

1. Perimeter (Р) ∆BDC (total length of all its sides) is calculated by the formula:

Perimeter ∆BDC = ВС + СD + ВD.

2. Perimeter ∆ABC = AB + BC + AC = 12 centimeters.

3. BD, being the median, divides the speaker into two equal parts. AD = CD. That is, AC = 2CD.

4. ∆АВС by the condition of the problem is isosceles. Therefore, its sides are equal. That is, AB = BC.

5. We replace in the formula for calculating the perimeter ∆АВС AB for ВС and АС for 2CD:

2BC + 2CD = 12 centimeters.

Sun + CD = 6 centimeters.

6. Substitute the resulting expression into the formula for calculating the perimeter ∆ВDС:

Perimeter ∆BDC = 6 + 5 = 11 centimeters.

Answer: perimeter ∆BDC = 11 centimeters.