In a right-angled triangle abc (c = 90 degrees) leg ac is 5 cm, and the median AM is 13 cm.

In a right-angled triangle abc (c = 90 degrees) leg ac is 5 cm, and the median AM is 13 cm. Find the hypotenuse AB.

The AFM triangle is rectangular, then, according to the Pythagorean theorem, we determine the length of the CM leg.

CM ^ 2 = AM ^ 2 – AC ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

CM = 12 cm.

Since the segment AM is the median of the triangle, then BM = CM = 12 cm.

Then BC = CM * 2 = 12 * 2 = 24 cm.

Let us determine the length of the hypotenuse AB in the triangle ABC.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 24 ^ 2 + 5 ^ 2 = 576 + 25 = 601.

AB = √601 cm.

Answer: The length of the hypotenuse AB is equal to √601 cm.