In a right-angled triangle ABC, the median CM is 8 cm, and the distance from the middle of leg AC

| February 22, 2021 | education

In a right-angled triangle ABC, the median CM is 8 cm, and the distance from the middle of leg AC to hypotenuse AB is 2 cm. Find the area of the triangle.

Since CM is the median of a right-angled triangle, drawn from a right angle to the hypotenuse, its length is equal to half the length of the hypotenuse, then CM = BM = AM = 8 cm, and AM = 2 * CM = 16 cm.

Determine the area of ​​the triangle AKM.

Sacm = AM * KN / 2 = 8 * 2/2 = 8 cm2.

The right-angled triangles ABC and AMK are similar in acute angle, since they have a common angle A.

Let’s determine the coefficient of similarity of triangles. K = AB / AM = 16/8 = 2.

The ratio of the areas of similar triangles is equal to the square of the similarity factor of the triangles. Savs / Sakm = K ^ 2 = 4.

Savs = 4 * 8 = 32 cm2.

Answer: The area of ​​the triangle is 32 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.