Question

ПОЖАЛУЙСТА ПОМОГИТЕ Плоскость a пересекает стороны АВ и ВС треугольника АВС в точках D и E соответственно,причем АС параллельна плоскости a . Найдите АС, если BD : AD = 2 : 3, DE = 15см.(нужен рисунок)

Answer 1

Ответ:

AC=DE*(AB/AD)=DE*((BD+AD)/BD=15*((2+3)/2)=37,5 см

Объяснение:

Answer 2

Finding the length of AC in a triangle

To find the length of AC in triangle ABC, where plane a intersects sides AB and BC at points D and E respectively, and AC is parallel to plane a, we can use the given information that BD:AD = 2:3 and DE = 15 cm.

Let's break down the problem step by step:

1. Draw a diagram of triangle ABC with points D and E on sides AB and BC respectively. Label the length of BD as 2x and the length of AD as 3x.


2. Since AC is parallel to plane a, we can conclude that triangles ABD and AEC are similar. This means that the ratios of corresponding sides are equal.

Using the given information, we have:

BD:AD = 2:3

Since the length of BD is 2x and the length of AD is 3x, we can write:

2x:3x = 2:3

3. Now, let's find the length of EC. Since triangles ABD and AEC are similar, the ratio of their corresponding sides is equal:

BD:EC = AD:AC

Substituting the given values, we have:

2x:EC = 3x:AC

4. We are given that DE = 15 cm. Using this information, we can find the value of EC:

EC = BC - BE

Since DE is parallel to BC, we can write:

EC = BC - DE

5. Now, let's substitute the values we have:

EC = BC - DE

EC = 3x - 15

6. Substituting this value into the previous equation, we have:

2x:3x = 3x:AC

Simplifying this equation, we get:

2x * AC = 3x * 3x

2x * AC = 9x^2

AC = (9x^2) / (2x)

AC = 9x / 2

7. Finally, let's substitute the given ratio BD:AD = 2:3:

2x / 3x = 2 / 3

Solving for x, we get:

x = 3

Substituting this value into the equation for AC, we have:

AC = 9 * 3 / 2

AC = 27 / 2

AC = 13.5 cm

Therefore, the length of AC in triangle ABC is 13.5 cm.

Note: The diagram provided is for illustrative purposes only. Please refer to the original question for the specific diagram.