The height of a right-angled triangle, drawn to the hypotenuse, divides it into 6cm 24cm segments. find the legs of the triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 24 centimeters. BE = 6 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 = √24 x 6 = √144 = 12 centimeters.

3. BC = √CE² + BE² = √12² + 6² = √144 + 36 = √180 = 6√5 centimeters.

4. AC = √CE² + AE² = √12² + 24² = √144 + 576 = √720 = 12√5 centimeters.

Answer: the legs of the triangle BC = 6√5 centimeters, AC = 12√5 centimeters.