Find the side of an isosceles triangle BCD if the base BC is 18 cm and the height CK is 12 cm.

We are given an isosceles triangle BCD, we know that its base BC is 18 cm, and the height CK is 12 cm.To calculate the side of the triangle, we apply the Pythagorean theorem to a right-angled triangle, which is formed by the lateral side of an isosceles triangle (the hypotenuse of the triangle) and the height and half of the base (the legs of the triangle).

In an isosceles triangle, the height is also the median and divides the bases into two equal parts:

18: 2 = 9 cm.

c ^ 2 = a ^ 2 + b ^ 2;

c = √ (a ^ 2 + b ^ 2) = √ (18 ^ 2 + 12 ^ 2) = √ (324 + 144) = √468 = 6√13 cm side.