Calculate the medians of a triangle with sides of 25cm. 25cm. 14cm.

In an isosceles triangle, the height drawn to the base is also the median of the triangle, then AP = CP = AC / 2 = 14/2 = 7 cm.

In a right-angled triangle ABP, we determine the length of the leg BP.

BP ^ 2 = AB ^ 2 – AP ^ 2 = 625 – 49 = 576.

BP = 24 cm.

Since the medians at the intersection point are divided in the ratio of 2/1, then OР = BC * / 3 = 24/3 = 8 cm.

Then, in the right-angled triangle AOP, we determine the length of the AO.

AO ^ 2 = AP ^ 2 + OP ^ 2 = 49 + 64 = 113.

AO = √113.

AO / MO = 2/1, then MO = AO / 2, and AM = AO + AO / 2 = √113 + √113 / 2 = 3 * √113 / 2.

Since the triangle is isosceles, then CК = AM = 3 * √113 / 2 cm.

Answer: The medians of the triangle are 24 cm and 3 * √113 / 2 cm.