The height of the right angle drawn to the hypotenuse divides it into 12 and 3 cm. Find the area.

univerkov | May 30, 2021 | education

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 12 cm. BE = 3 cm. S is the area of the triangle.

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 = √12 x 3 = 6 cm.

3. ВС = √CE² + BE² (by the Pythagorean theorem).

BC = √6² + 3² = √36 + 9 = √45 = 3√5 cm.

4. AC = √CE² + AE² = √6² + 12² = √36 + 144 = √180 = 6√5 cm.

5. S triangle = AC x BC / 2 = 3√5 x 6√5 / 2 = 45 cm².

Answer: S of a triangle is 45 cm².

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.