Question

Дано: параллелограм АBCD из точки В опусти прямую и обозачим Е угол ВАЕ = 30 градусам, AD=BC, AB=CD, AB=5 см, ED=2AE. Найти Р параллелограма АВСD

Answer 1

Решение:

Р= 2(a+b)

АЕ= АВ * cos<А = 5 *0.9=4.5 см

В прямоугольном треугольнике сторона лежащая против <30 градусов равна половине гипотинузы отсюда следует сто ВЕ = половине АВ =2.5

АЕ = 4.5 см

отсюда следует что АD = 4.5 * 2 = 9

Р = 2(9+5) = 28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Given Information:

We are given a parallelogram ABCD, where point E is dropped from point B on a line and angle BAE is equal to 30 degrees. It is also given that AD is equal to BC, AB is equal to CD, AB is 5 cm, and ED is equal to 2 times AE. We need to find the perimeter of parallelogram ABCD.

Solution:

To find the perimeter of parallelogram ABCD, we need to find the lengths of all four sides and then add them together.

Let's start by finding the length of side AB. We are given that AB is equal to 5 cm.

Next, let's find the length of side BC. Since AD is equal to BC, we can use the length of AB to find the length of BC. Since AB is equal to CD, we can conclude that BC is also equal to CD. Therefore, BC is also equal to 5 cm.

Now, let's find the length of side AD. Since AD is equal to BC, AD is also equal to 5 cm.

Finally, let's find the length of side DC. Since AB is equal to CD, DC is also equal to 5 cm.

Now, let's find the length of AE. We are given that ED is equal to 2 times AE. Let's assume AE is x. Therefore, ED is equal to 2x. Since ED is equal to 2 times AE, we can write the equation as 2x = ED. Given that ED is equal to 2 times AE, we can substitute 2x with 2 times AE. Therefore, 2x = 2(AE). Simplifying this equation, we get x = AE.

Now, let's find the length of AE. We are given that angle BAE is equal to 30 degrees. Since angle BAE is equal to angle AEB (opposite angles in a parallelogram are equal), we can conclude that angle AEB is also equal to 30 degrees. Since angle AEB is equal to angle AED (vertical angles are equal), we can conclude that angle AED is also equal to 30 degrees. Therefore, triangle AED is an equilateral triangle. In an equilateral triangle, all sides are equal. Therefore, AE is equal to ED, which is equal to 2x.

Now, let's substitute the value of AE in terms of x into the equation AE = ED = 2x. We get x = 2x. Solving this equation, we get x = 0. Therefore, AE is equal to 0.

Since AE is equal to 0, we can conclude that the length of side AE is 0.

Now, let's find the perimeter of parallelogram ABCD by adding the lengths of all four sides:

Perimeter = AB + BC + CD + DA = 5 cm + 5 cm + 5 cm + 5 cm = 20 cm

Therefore, the perimeter of parallelogram ABCD is 20 cm.