Question

В параллелограмме АВСД проведена биссектриса угла АВС, которая пересекает сторону СД в точке Е. Найдите АВ, если СЕ=15см, а периметр параллелограмма равен 60см. Помогите пожалуйста.

Answer 1

Решение на фото.Решение на фото.

Answer 2

Problem Analysis

We are given a parallelogram ABCD, where the angle bisector of angle ABC intersects side CD at point E. We are also given that CE = 15 cm and the perimeter of the parallelogram is 60 cm. We need to find the length of AB.

Solution

To find the length of AB, we need to use the given information and some properties of parallelograms.

Let's denote the length of AB as x.

Since ABCD is a parallelogram, opposite sides are equal. Therefore, AD = BC = x.

We are also given that the perimeter of the parallelogram is 60 cm. The perimeter of a parallelogram is the sum of all its sides. In this case, it is given by:

Perimeter = AB + BC + CD + DA

Substituting the values we know:

60 = x + x + CD + x

Simplifying the equation:

60 = 3x + CD

We are also given that CE = 15 cm. Since CE is the angle bisector of angle ABC, it divides side AD into two equal segments. Therefore, AD = DE = 15 cm.

Using this information, we can write:

CD = CE + DE = 15 + 15 = 30 cm

Substituting this value back into the equation:

60 = 3x + 30

Simplifying the equation further:

3x = 60 - 30 3x = 30 x = 30 / 3 x = 10

Therefore, the length of AB is 10 cm.

Answer

The length of AB in the parallelogram ABCD is 10 cm.