Question

Периметр прямоугольника равен 70 см. Найдите измерения прямоугольника, если известно, что, увеличив длину на 10 см, получим удвоенную ширину прямоугольникаПомогите, пожалуйста

Answer 1

А- длина
в- ширина

2(а+в)=70
а+10=2в

а+в=35
а=35-в

а=2в-10

35-в=2в-10
3в=45
в=15

а+10=2в
а=20

Answer 2

Problem Analysis

We are given that the perimeter of a rectangle is 70 cm. We need to find the dimensions of the rectangle, given that increasing the length by 10 cm results in the width being doubled.

Solution

Let's assume the length of the rectangle is L and the width is W.

The perimeter of a rectangle is given by the formula: Perimeter = 2(L + W).

We are given that the perimeter is 70 cm, so we can write the equation as: 70 = 2(L + W).

We are also given that increasing the length by 10 cm results in the width being doubled. Mathematically, we can express this as: W = 2(L + 10).

Now we have two equations with two variables. We can solve this system of equations to find the values of L and W.

Solving the Equations

Let's substitute the value of W from the second equation into the first equation:

70 = 2(L + 2(L + 10))

Simplifying the equation:

70 = 2(3L + 20)

70 = 6L + 40

Subtracting 40 from both sides:

30 = 6L

Dividing both sides by 6:

L = 5

Now, let's substitute the value of L into the second equation to find W:

W = 2(5 + 10)

W = 2(15)

W = 30

Answer

The dimensions of the rectangle are: - Length: 5 cm - Width: 30 cm

Please let me know if I can help you with anything else.