The side of the triangle ABC is crossed by the straight line MN || AC. The perimeters of triangles ABC
| September 3, 2021 | education
The side of the triangle ABC is crossed by the straight line MN || AC. The perimeters of triangles ABC and MBN are in a ratio of 3: 1. The ABC area is 144. What is the area of MBN?
Since, by condition, МН is parallel to АС, the triangles ABC and МBН are similar in two angles. The angle B in triangles is common, the angle BMN = BAC as the corresponding angles at the intersection of parallel straight lines МН and АС secant AB.
The perimeters of such triangles are referred to as a coefficient of similarity, then Rmvn / Ravs = K = 1/3.
The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.
Smvn / Savs = K ^ 2 = 1/9.
Smvn = Savs / 9 = 144/9 = 16 cm2.
Answer: The area of the MВН triangle is 16 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.
