In isosceles △abc (ac = bc) with base angle 30° cd is a median. how long is the leg of △abc, if sum of the perimeters of △acd and △bcd is 20 cm more than the perimeter of △abc?

Note necessary facts about isosceles triangle ABC:

1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.

AC=2CD.

2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.

BC=2CD.

3. Find the perimeters of triangles ACD, BCD and ABC:

4.  If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then

5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.

20 cm.

6hryt%4578855