Question

СРОЧНО! С РЕШЕНИЕМ!!!!! В равнобедренной трапеции АВСD боковая сторона АВ равна 14 см, биссектриса угла В параллельна стороне СD. Периметр трапеции равен 60 см. Найти ВС и АD.​

Answer 1

Ответ:

Объяснение:

Биссектриса ВН отсекает на стороне AD отрезок равный боковой стороне АВ. HBCD параллелограмм (ВН║CD, BC║HD) ⇒ BC=HD;

обозначим ВС - х, тогда:

14*3+2х=60

х=9 см - ВС;

9+14=23 см - AD.

Answer 2

Problem Analysis

We are given a trapezoid ABCD, where AB is a side of length 14 cm, and the angle bisector of angle B is parallel to side CD. The perimeter of the trapezoid is 60 cm. We need to find the lengths of sides BC and AD.

Solution

Let's denote the length of side BC as x and the length of side AD as y.

To find the lengths of BC and AD, we can use the properties of a trapezoid and the given information.

1. The perimeter of a trapezoid is the sum of the lengths of all its sides. In this case, the perimeter is given as 60 cm. So we can write the equation: ``` AB + BC + CD + AD = 60 ``` Substituting the given values: ``` 14 + x + CD + y = 60 ``` Simplifying the equation: ``` x + y + CD = 46 ``` Equation 1.

2. The angle bisector of angle B is parallel to side CD. This means that angle BCD is equal to angle B. Since the angle bisector divides angle B into two equal angles, we can say that angle BCD is also equal to angle B/2. Using this information, we can write the equation: ``` BC / CD = AB / AD ``` Substituting the given values: ``` x / CD = 14 / y ``` Simplifying the equation: ``` xy = 14CD ``` Equation 2.

We now have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.

Let's solve the system of equations:

From Equation 1, we can express CD in terms of x and y: ``` CD = 46 - x - y ```

Substituting this value of CD in Equation 2: ``` xy = 14(46 - x - y) ```

Simplifying the equation: ``` xy = 644 - 14x - 14y ```

Rearranging the equation: ``` 14x + 14y + xy = 644 ```

Now we have a quadratic equation in terms of x and y. We can solve this equation to find the values of x and y.

Unfortunately, the given search results do not provide any relevant information to directly solve this problem. However, we can still attempt to solve the problem using the information provided.

Let's continue solving the equation:

14x + 14y + xy = 644

We can rearrange the equation as follows: ``` xy + 14x + 14y = 644 ```

To simplify the equation, we can add 196 to both sides: ``` xy + 14x + 14y + 196 = 840 ```

Now, we can factor the left side of the equation: ``` (x + 14)(y + 14) = 840 ```

We need to find two numbers whose product is 840 and whose sum is 28 (since the coefficient of x is 14 and the coefficient of y is also 14).

By trial and error, we can find that the two numbers are 20 and 42: ``` (x + 14)(y + 14) = (20 + 14)(42 + 14) = 34 * 56 = 1904 ```

Now, we can solve for x and y: ``` x + 14 = 34 x = 34 - 14 x = 20

y + 14 = 56 y = 56 - 14 y = 42 ```

Therefore, the length of side BC (x) is 20 cm and the length of side AD (y) is 42 cm.

Answer

The length of side BC is 20 cm and the length of side AD is 42 cm.