The perimeter of an isosceles triangle is 90 cm, and the height drawn to the base is 15 cm. Find the sides of the triangle.

Let the side of the triangle be equal to a. Then the base is equal to perimeter – 2a = 90-2a.
Since the triangle is isosceles and the height is drawn to its base, it is the same median and bisector and divides the original triangle into 2 equal ones. So, if the median has been drawn, then the opening distance = 45-a.
Consider a triangle formed by side, half base, and height. It is rectangular because the height is perpendicular to the base. By the Pythagorean theorem a ^ 2 = 15 ^ 2 + (45-a) ^ 2. Hence a = 25, then 45-a = 20.
90-2a = 40
Answer: 25, 25, 40.