# Find the perimeter of triangle ABC (AB = BC) if the median BM = 11 cm.The perimeter of triangle ABM is 34 cm.

August 23, 2021 | education

| 1. Р – perimeter (total length of all sides).

2. P of triangle ABC = AB + BC + AC.

AB = BC according to the condition of the problem.

AM = CM, since the median BM divides the AC side into two equal segments. AC = 2AM.

3. Replace AC with 2AM, BC with AB:

P triangle ABC = AB + AB + 2AM = 2 (AB + AM).

4. P triangle ABM = AB + AM + BM = 34 centimeters.

AB + AM = 34 – BM = 34 – 11 = 23 centimeters.

5. P triangle ABC = 2 x 23 = 46 centimeters.

Answer: P of triangle ABC is 46 centimeters.

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