Question

Периметр прямоугольника равен 20 м в квадрате . Площадь прямоугольника 21 м в квадрате. Найти стороны прямоугольников?

Answer 1

Площадь считается по формуле:
a*b=21
Периметр:
(a+b)*2=20 / :2 (делим на два обе части)

a+b=10 (1)
a*b=21 (2)
 
Выражаем из (1) а
а=10-b
Подставляем в выражение (2)
b(10-b)=21
b²-10b+21=0
D=100-(4*1*21)=16=4²
b1=10+4/2=7, значит а=3
b2=10-4/2=3, значит а =7
Ответ: 7 и 3 см

Answer 2

3 и 7 см , т.к.
Площадь прямоугольника
S=ab, 3*7=21
Периметр прямоугольника
Р=2(а+b)
2(3+7)=20

Answer 3

Finding the sides of a rectangle given the perimeter and area

To find the sides of a rectangle given the perimeter and area, we can use the formulas for perimeter and area of a rectangle.

Let's denote the length of one side of the rectangle as 'a' and the length of the other side as 'b'.

The perimeter of a rectangle is given by the formula: Perimeter = 2(a + b) The area of a rectangle is given by the formula: Area = a * b From the given information, we know that the perimeter of the rectangle is 20 m² and the area is 21 m².

Let's solve for the sides of the rectangle using these formulas.

Solving for the sides of the rectangle

Given: Perimeter = 20 m² Area = 21 m²

Using the formulas for perimeter and area, we can set up the following equations:

Equation 1: Perimeter = 2(a + b) Equation 2: Area = a * b

Substituting the given values into the equations, we have:

Equation 1: 20 = 2(a + b) Equation 2: 21 = a * b

Now, we have a system of two equations with two variables. We can solve this system to find the values of 'a' and 'b'.

To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can express 'a' in terms of 'b':

a = (20 - 2b) / 2

Substituting this expression for 'a' into Equation 2, we have:

21 = [(20 - 2b) / 2] * b

Simplifying the equation, we get:

42 = 20b - 2b²

Rearranging the equation, we have:

2b² - 20b + 42 = 0

Now, we can solve this quadratic equation to find the values of 'b'. We can use the quadratic formula:

b = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = -20, and c = 42.

Solving for 'b', we get two possible values:

b₁ ≈ 6.82 b₂ ≈ 1.18

Now, we can substitute these values of 'b' back into Equation 1 to find the corresponding values of 'a'.

For b₁ ≈ 6.82: a₁ = (20 - 2 * 6.82) / 2 ≈ 3.18

For b₂ ≈ 1.18: a₂ = (20 - 2 * 1.18) / 2 ≈ 8.82

Therefore, the sides of the rectangle are approximately: a₁ ≈ 3.18 m and b₁ ≈ 6.82 m or a₂ ≈ 8.82 m and b₂ ≈ 1.18 m

Please note that these values are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.