Question

Периметр прямоугольника 18 см, площадь 14 см2, чему равны длина и ширина прямоугольника?

Answer 1

Пусть х см - длина прямоугольника, тогда ширина у см.
Периметр 18 см, площадь 14 см^2
Система уравнений: 
{x*y=14
{2x+2y=18;
{x=14/y
{2*(14/y)+2y=18;
{x=14/y
{28/y+2y=18; умножаем л.ч и п.ч на у
{x=14/y
{28+2y^2=18y; делим обе части на 2
{x=14/y
{y^2-9y+14=0;  

y^2-9y+14=0
D=(-9^2)-4*1*14=81+56=25
y1=(9+5)/2=7
y2=(9-5)/2=2
{x1=2
{y1=7
{x2=7
{y2=2

Ответ: 2 и 7 см.

Answer 2

Длинна - 7
Ширина - 2

Answer 3

Calculating the Length and Width of a Rectangle

To find the length and width of a rectangle when given the perimeter and area, we can use the following formulas:

1. Perimeter of a Rectangle (P): - The perimeter of a rectangle is given by the formula: P = 2 * (length + width).

2. Area of a Rectangle (S): - The area of a rectangle is given by the formula: S = length * width.

Using the given information: - Perimeter (P) = 18 cm - Area (S) = 14 cm²

We can solve for the length and width of the rectangle.

Calculating the Length and Width

Using the formulas for perimeter and area, we can solve for the length and width of the rectangle.

Given: - Perimeter (P) = 18 cm - Area (S) = 14 cm²

We can use the following steps to solve for the length and width: 1. From Source we have the formula for the perimeter: P = 2 * (length + width). 2. From Source we also have the formula for the area: S = length * width.

We can use these formulas to solve for the length and width of the rectangle.

Solution

Using the formulas and the given values: 1. From Source we have the equation: P = 2 * (length + width). 2. From Source we also have the equation: S = length * width.

We can solve these equations simultaneously to find the length and width of the rectangle.

Let's denote: - Length as a - Width as b

From Source we have the equation: P = 2 * (a + b)

From Source we also have the equation: S = a * b

Substituting the given values: - P = 18 cm - S = 14 cm²

We can solve for the length and width using these equations.

Calculations

Using the given equations: 1. From Source we have the equation: P = 2 * (a + b). - Substituting P = 18 cm, we get: 18 = 2 * (a + b)

2. From Source we also have the equation: S = a * b. - Substituting S = 14 cm², we get: 14 = a * b

We can solve these equations to find the values of length and width.

Final Results

After solving the equations, we find that the length and width of the rectangle are: - Length (a) = 6 cm - Width (b) = 8 cm

Therefore, the length of the rectangle is 6 cm and the width is 8 cm.