Question

Я могу задать 14 вопросов по 100 баллов с этим заданием. Высшие умы математики, помогите мне, обычному смертному по ГЕОМЕТРИИ. Даю все сто баллов. Пожалуйста будьте честны и без плагиата. У меня проблемы с этим заданием. В параллелограмме ABCD, периметр которого равен 40, проведена биссектриса BN. Отрезок ND равен половине отрезка CD. Постройте чертеж и найдите стороны параллелограмма. решите пожалуйста

Answer 1

Ответ: AB и CD – 8 (ед. длины); BC и AD – 12 (ед. длины)

Объяснение:

   ND=CD/2 Примем ND=a.  Тогда CD=2a, AB=CD=2a.

ВС||AD, BN – секущая => ∠СВN=∠BNA – накрестлежащие при пересечении параллельных прямых секущей. Но ∠СВN=∠АВN как половина угла АВС ( BN – биссектриса) =>

∠ANB=∠АВN.

   В треугольнике АВN углы при основании BN равны. ∆ АВN- равнобедренный. => AN=AB=2a =>

 AD=AN+ND=2a+a=3a.  BC=AD=3a

P(ABCD)=AB+CD+BC+AD=2•(2a+3a)=10a

10a=40

a=4

AB=CD=2•4=8 (ед. длины)

BC=AD=3•4=12 (ед. длины)

Answer 2

Parallelogram with Bisector

To solve the problem, let's start by understanding the given information. We have a parallelogram ABCD with a perimeter of 40 units. A bisector BN is drawn, and the length of segment ND is equal to half the length of segment CD.

To find the sides of the parallelogram, we can use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length. Therefore, we can conclude that:

AB = CD (opposite sides of a parallelogram are equal)

Since the perimeter of the parallelogram is given as 40 units, we can express this in terms of the sides:

2(AB + BC) = 40 (perimeter formula for a parallelogram)

Now, let's use the information about segment ND. We know that the length of segment ND is equal to half the length of segment CD. Mathematically, we can express this as:

ND = 1/2 * CD

Since opposite sides of a parallelogram are equal, we can also say that:

BC = AD

Now, we can rewrite the perimeter formula using the given information:

2(AB + BC) = 40

Substituting BC with AD:

2(AB + AD) = 40

We also know that ND is equal to half the length of CD:

ND = 1/2 * CD

Now, let's solve the equations to find the values of AB, BC, AD, and CD.

To solve the equations, we need to use the fact that the sum of the opposite sides of a parallelogram is equal to the perimeter. In this case, the sum of AB and CD is equal to the perimeter, which is 40 units.

Let's solve the equations step by step:

1. From the equation 2(AB + AD) = 40, we can simplify it to AB + AD = 20.

2. From the equation ND = 1/2 * CD, we can substitute ND with 1/2 * CD in the equation AB + AD = 20 to get AB + AD = 1/2 * CD.

3. Since opposite sides of a parallelogram are equal, we can say that AB = CD. Substituting AB with CD in the equation AB + AD = 1/2 * CD, we get CD + AD = 1/2 * CD.

4. Simplifying the equation CD + AD = 1/2 * CD, we get AD = -1/2 * CD.

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