The height drawn from the apex of the right angle of a right-angled triangle divides the hypotenuse

The height drawn from the apex of the right angle of a right-angled triangle divides the hypotenuse into 5 cm and 15 cm segments. What is the smaller leg of the triangle?

1. A, B, C – the vertices of the triangle. ∠С = 90 °. AE = 5 centimeters. BE = 15 centimeters, CE – height.

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 15 = 5√3 centimeters.

3. BC = √CE² + BE² = √ (5√3) ² + 15² = √75 + 225 = √300 = 10√3 centimeters.

4. AC = √CE² + AE² = √ (5√3) ² + 5² = √75 + 25 = √100 = 10 centimeters.

Answer: AC = 10 centimeters – smaller leg.