In an isosceles triangle abc, the base is ac = 24 cm and the median is bd = 5 cm. Find the sides.

Since triangle ABC is isosceles, its median BD is also the height of the triangle, and then triangles ABD and BCD are rectangular.

The median BD divides the base of the AC into two equal segments. АD = СD = АС / 2 = 24/2 = 12 cm.

From the right-angled triangle ВСD, according to the Pythagorean theorem, we determine the length of the hypotenuse ВС.

ВС ^ 2 = ВD ^ 2 + СD ^ 2 = 25 + 144 = 169.

BC = 13 cm.

Since ABC is an isosceles triangle, AB = BC = 13 cm

Answer: The length of the sides is 13 cm.