In the trapezium, the lower base is 5 times larger than the upper one. The segment MN parallel to the bases

| February 6, 2021 | education

In the trapezium, the lower base is 5 times larger than the upper one. The segment MN parallel to the bases (points M and N lie on the lateral sides) is 4 times larger than the upper base. In what ratio does the segment MN divide the height of the trapezoid?

Let the length of the smaller base be X cm, then the length of the larger base is 5 * X, and the length of the segment MН = 4 * X cm.

Determine the area of the trapezium AВСD.

Savsd = (X + 5 * X) * ВН / 2 = 3 * X * ВН.

Since ВН = (ВK + НK), then Savsd = 3 * X * (ВK + НK).

The area of the trapezoid MBCН is equal to:

Smvcn = (X + 4 * X) * ВK / = 5 * X * ВK / 2 = 2.5 * X * ВK.

The area of the trapezoid AMНD is equal to:

Samnd = (4 * X + 5 * X) * НK / 2 = 4.5 * X * NK.

Then Smvsn + Samnd = Savsd.

2.5 * X * ВK + 4.5 * X * НK = 3 * X * (ВK + НK).

4.5 * НK – 3 * НK = 3 * ВK – 2.5 * ВK.

1.5 * НK = 0.5 * ВK.

НK / ВK = 1/3.

Answer: The MН segment divides the height by a ratio of 1/3.



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.