The height of an isosceles triangle is 6 cm, and the base is 34 cm. What is the lateral side?

Let the side be x.
The height of an isosceles triangle, drawn to the base, divides the base in half. 34/2 = 17 cm.
The lateral side of this isosceles triangle is the hypotenuse, and the height and half of the base are the legs of the right triangle. Since the sum of the squares of the legs is equal to the square of the hypotenuse, we can write:
6 ^ 2 + 17 ^ 2 = x ^ 2;
36 + 289 = x ^ 2;
325 = x ^ 2.
The desired side length is equal to the square root of 325.