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 °. AK = 5 centimeters. BK = 15 centimeters.

CK – height.

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

CK = √AK x BK = √5 x 20 = 10 centimeters.

3. BC = √CK² + BK² = √10² + 20² = √100 + 400 = √500 = 10√5 centimeters.

4. AC = √CK² + AK² = √10 ² + 5² = √100 + 25 = √125 = 5√5 centimeters.

Answer: the legs of the triangle BC = 10√5 centimeters, AC = 5√5 centimeters.