Find the lengths of the legs of a right-angled triangle if the height drawn from a right

Find the lengths of the legs of a right-angled triangle if the height drawn from a right angle divides the hypotenuse into two segments 6 cm and 24 cm.

1. Vertices of the triangle – A, B, C. ∠C = 90 °. CH – height. AH = 6 cm. BH = 24 cm.

2. The height drawn to the hypotenuse of a right-angled triangle, according to its properties,

calculated by the formula:

CH = √АH x BH = 6 x 24 = √144 = 12 cm.

3. AC = √АH² + CH² (by the Pythagorean theorem).

AC = √6² + 12² = √36 + 144 = √180 = √36 x 5 = 6√5 cm.

4. ВС = √ВН² + СН² (by the Pythagorean theorem).

BC = √24² + 12² = √576 + 144 = √720 = √144 x 5 = 12√5 cm.

Answer: leg AC = 6√5 cm, leg BC = 12√5 cm.