Question

периметр четырёхугольника равен 20 см .Найдите стороны четырёхугольника , если одна из них составляет 40% периметра, а три оставшихся равны​

Answer 1

Ответ:

8 см, 4 см, 4 см, 4 см

Пошаговое объяснение:

1)40%=0.4

20*0.4=8(см) - первая сторона

2)20-8=12(см) - сума трьох остальных сторон

3)12/3=4(см) - длина одной из остальных трёх сторон

Answer 2

Perimeter of a Quadrilateral

The perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, we are given that the perimeter of the quadrilateral is 20 cm. Let's denote the lengths of the sides of the quadrilateral as a, b, c, and d.

Relationship between Side Lengths and Perimeter

We are also given that one of the sides of the quadrilateral is 40% of the perimeter, and the remaining three sides are equal. Let's use this information to set up an equation.

The length of one side, a, is 40% of the perimeter, which can be written as:

a = 0.40 * (a + b + c + d)

The remaining three sides, b, c, and d, are equal, so we can write:

b = c = d = (1 - 0.40) * (a + b + c + d) / 3

Solving the Equations

To find the lengths of the sides of the quadrilateral, we need to solve these two equations simultaneously.

Let's substitute the value of b in terms of a into the equation for side a:

a = 0.40 * (a + (1 - 0.40) * (a + b + c + d) / 3 + c + d)

Simplifying the equation, we get:

a = 0.40 * (a + 0.60 * (a + 2b + 2c + 2d) / 3)

Now, let's substitute the value of a in terms of b, c, and d into the equation for side b:

b = (1 - 0.40) * (a + b + c + d) / 3

Substituting the value of a from the previous equation, we get:

b = (1 - 0.40) * (0.40 * (a + 0.60 * (a + 2b + 2c + 2d) / 3) + b + c + d) / 3

Simplifying the equation, we get:

b = (1 - 0.40) * (0.40 * (0.40 * (a + 0.60 * (a + 2b + 2c + 2d) / 3) + b + c + d) + b + c + d) / 3

We can now simplify and solve these equations to find the values of a, b, c, and d.