Question

Площина у паралельна стороні АВ трикутника ABC та перетинає сторони AC i BC в точках A1, B1, відповідно. Знайдіть довжину відрізка ВС, якщо AB = BB 9 см A1 B1 = 3 см. СРОЧНОООО​

Answer 1

Ответ:

Bb = 9см + A1B1 3 см / 2 = 6см

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given a triangle ABC, and there is a plane parallel to side AB that intersects sides AC and BC at points A1 and B1, respectively. We need to find the length of segment BC given that AB = 9 cm and A1B1 = 3 cm.

Solution

To find the length of segment BC, we can use the concept of similar triangles. Since the plane is parallel to side AB, we can consider triangle ABC and triangle A1B1C as similar triangles.

Let's denote the length of segment BC as x.

Using the concept of similar triangles, we can set up the following proportion:

AB / A1B1 = BC / BC1

Substituting the given values, we have:

9 cm / 3 cm = x / BC1

Simplifying the equation, we get:

3 = x / BC1

To find the value of BC1, we need to find the length of segment A1C1. Since the plane is parallel to side AB, segment A1B1 is parallel to segment AC. Therefore, we can consider triangle A1B1C and triangle AC1B as similar triangles.

Using the concept of similar triangles, we can set up the following proportion:

A1B1 / AC1 = B1C / BC

Substituting the given values, we have:

3 cm / AC1 = x / 9 cm

Simplifying the equation, we get:

AC1 = (3 cm * 9 cm) / x

Now, let's find the value of AC1. Since segment A1B1 is parallel to segment AC, we can use the concept of alternate interior angles to find the value of AC1.

Using the alternate interior angles theorem, we know that angle A1B1C is equal to angle ACB. Therefore, triangle A1B1C and triangle ACB are similar triangles.

Using the concept of similar triangles, we can set up the following proportion:

A1B1 / AB = B1C / BC

Substituting the given values, we have:

3 cm / 9 cm = x / BC

Simplifying the equation, we get:

BC = (9 cm * x) / 3 cm

Now, we can substitute the value of BC in the equation for AC1:

AC1 = (3 cm * 9 cm) / [(9 cm * x) / 3 cm]

Simplifying the equation, we get:

AC1 = 27 cm / x

Now, we can substitute the value of AC1 in the equation for BC1:

3 = x / [(27 cm / x)]

Simplifying the equation, we get:

3 = x^2 / 27 cm

Multiplying both sides of the equation by 27 cm, we get:

81 cm = x^2

Taking the square root of both sides of the equation, we get:

x = √81 cm

Therefore, the length of segment BC is 9 cm.

Answer

The length of segment BC is 9 cm.

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