Question

В параллелограмме АВСД биссектриса тупого угла В пересекает сторону АД в точке F. Найти периметр параллелограмма, если АВ=12 и AF:FД=4:3. Помогите пожалуйста решить срочно нужно

Answer 1

BFA=CBF(как накрест лежащие ),тогда треугольник ABF равнобедренный и AF =12

Answer 2

Problem Analysis

We are given a parallelogram ABCD, where the bisector of angle B intersects side AD at point F. We need to find the perimeter of the parallelogram if AB = 12 and AF:FD = 4:3.

Solution

To find the perimeter of the parallelogram, we need to know the lengths of all four sides. Let's analyze the given information step by step.

1. We are given that AB = 12. This means that AD is also equal to 12, as opposite sides of a parallelogram are equal in length.

2. We are also given that AF:FD = 4:3. Let's assume that AF is 4x and FD is 3x, where x is a common factor. This means that the length of AF is 4x and the length of FD is 3x.

3. Since the bisector of angle B intersects side AD at point F, we can conclude that triangle ABF is similar to triangle CDF. This is because the bisector of an angle divides the opposite side of a triangle into segments that are proportional to the adjacent sides.

4. Using the similarity of triangles ABF and CDF, we can set up the following proportion:

AB/CD = AF/FD

Substituting the known values, we get:

12/CD = 4x/3x

Simplifying the equation, we get:

12/CD = 4/3

Cross-multiplying, we get:

3 * 12 = 4 * CD

Solving for CD, we get:

CD = (3 * 12) / 4 = 9

Therefore, CD is equal to 9.

5. Now that we know the lengths of AB and CD, we can calculate the perimeter of the parallelogram. The perimeter is the sum of all four sides:

Perimeter = AB + BC + CD + DA

Since opposite sides of a parallelogram are equal in length, we have:

Perimeter = AB + AB + CD + CD

Substituting the known values, we get:

Perimeter = 12 + 12 + 9 + 9 = 42

Therefore, the perimeter of the parallelogram is 42 units.

Answer

The perimeter of the parallelogram ABCD is 42 units.