The height of a right-angled triangle drawn to the hypotenuse divides it into segments 40 and 10 cm long, find the legs of the triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 40 centimeters. BE = 10 centimeters.
2. We calculate the length of the height CE, which, according to the properties of a right-angled triangle, is calculated by the formula:
CE = √AE x BE = √40 x 10 = √400 = 20 centimeters.
3. BC = √CE² + BE² = √20² + 10² = √400 + 100 = √500 = 10√5 centimeters.
4. AC = √CE² + AE² = √20² + 40² = √400 + 1600 = √2000 = 20√5 centimeters.
Answer: the legs of the triangle BC = 10√5 centimeters, AC = 20√5 centimeters.