In an isosceles triangle, the height dropped to the base is 4 cm, and the base is 4 cm, find the side.

Since the triangle is isosceles, the height dropped to the base is also the median, that is, it divides the base into two equal parts. Height forms a right angle with the base of the triangle. Then the lateral side of the triangle, which lies opposite the 90 degree angle, is the hypotenuse, and the height and half of the base are the adjacent legs.
Find the length of the leg at the base:
4: 2 = 2 (cm).
Let us find the length of the hypotenuse by the Pythagorean theorem:
hypotenuse ^ 2 = 4 ^ 2 + 2 ^ 2;
hypotenuse ^ 2 = 16 + 4;
hypotenuse ^ 2 = 25;
hypotenuse = 5 (cm).