The height drawn to the hypotenuse divides it into segments 5 cm and 20 cm long. Find the legs of the triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 5 centimeters.

BE = 20 centimeters.

2. According to the properties of a right-angled triangle, the height CE, drawn from the vertex of the right angle, is calculated by the formula:

CE = √AE x BE = √5 x 20 = 10 centimeters.

3. ВС = √CE² + BE² (by the Pythagorean theorem).

BC = √10² + 20² = √100 + 400 = √500 = 10√5 centimeters.

4. AC = √CE² + AE² = √10² + 5² = √100 + 25 = √125 = 5√5 centimeters.

Answer: leg BC = 10√5 centimeters, leg AC = 5√5 centimeters.