Question

В трапеции ABCD основание в три раза больше, чем BC. Точка М делит сторону CD в отношении СМ : MD = 1:2. Определите вкаком отношении отрезки АМ и BD делятся точкой их пересечения.​ ПОМОГИТЕ ПОЖАЛУЙСТА!!!

Answer 1

Ответ:

Объяснение:

Определите вкаком отношении отрезки АМ и BD делятся точкой их пересечения.​ П

Answer 2

Problem Analysis

We are given a trapezoid ABCD, where the base AB is three times larger than BC. Point M divides side CD in the ratio CM:MD = 1:2. We need to determine the ratio in which the segments AM and BD are divided by their intersection point.

Solution

Let's assume that BC has a length of x. Since AB is three times larger than BC, we can say that AB = 3x.

We are also given that CM:MD = 1:2. Let's assume that CM = y. Therefore, MD = 2y.

To find the ratio in which AM and BD are divided by their intersection point, we need to find the lengths of AM and BD.

Using the fact that AB is parallel to CD, we can say that triangles ABC and AMD are similar. Therefore, we can set up the following proportion:

AM/AB = MD/BC

Substituting the given values, we have:

AM/3x = 2y/x

Cross-multiplying, we get:

AM * x = 3x * 2y

Simplifying, we have:

AM = 6y

Similarly, using the fact that AB is parallel to CD, we can say that triangles ABD and CMD are similar. Therefore, we can set up the following proportion:

BD/AB = CM/CD

Substituting the given values, we have:

BD/3x = y/(x + 3x)

Simplifying, we have:

BD/3x = y/4x

Cross-multiplying, we get:

BD * 4x = 3x * y

Simplifying, we have:

BD = 3/4 * y

Therefore, the ratio in which AM and BD are divided by their intersection point is:

AM:BD = 6y : 3/4 * y

Simplifying, we have:

AM:BD = 8:3

So, the segments AM and BD are divided in the ratio of 8:3 by their intersection point.

Answer

The segments AM and BD are divided in the ratio of 8:3 by their intersection point.