In an isosceles triangle, the lateral side is 15 cm, the height drawn to the base is 12 cm. Find the base.

Since the height is perpendicular to the base, it creates an angle of 90 degrees. Therefore, the resulting triangles are rectangular. We can use the Pythagorean theorem to find the line segments into which the base divides the height. To do this, we introduce the variables a, b, c, which will denote the sides of the triangle and the height h.

Since the triangle is isosceles, the segments of side c are equal to each other. Let us denote them by o and e. Find the segment of the base with: o = e = √ (a2 – h2) = √ (225 – 144) = √81 = 9.

The segments are equal, so: c = 9 + 9 = 18.

Answer: 18.