Triangle ABC is isosceles with base AC. Find the base if the median BM is 12 cm and the side is 13 cm.

univerkov | September 2, 2021 | education

Since the triangle ABC is isosceles, the median of the BM is also the height, then the BM is perpendicular to the AC.

From the right-angled triangle BMC, according to the Pythagorean theorem, we determine the leg CM.

CM ^ 2 = BC ^ 2 – BM ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.

CM = 5 cm.

Then the base AC = 2 * CM = 2 * 5 = 10 cm.

Answer: The length of the base of the AC = 10 cm.

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