The median of an isosceles triangle, drawn to its base, is 5 cm. The base is 24 cm. Find the side of the triangle.

An isosceles triangle is a triangle in which the sides are equal.

The median of an isosceles triangle, drawn to its base, is also the bisector and height.

Thus, two equal right-angled triangles are based: ΔАВМ and ΔМВС.

Consider a triangle ΔABM. To calculate AB, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BM ^ 2 + AM ^ 2;

AM = AC / 2;

AM = 24/2 = 12 cm;

AB ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169;

AB = √169 = 13 cm.

Answer: the length of the side of the triangle is 13 cm.