Question

Периметр прямоугольника 50 см. Как найти 1 сторону прямоугольника? Верно ли утверждение, что его площадь может быть равна 24 см2?

Answer 1

Да, может.
Подтвердим это системой уравнений. Пусть одна сторона х, а другая у. Тогда периметр будет равен 2х+2у=50 см, а площадь ху=24 см^2. Составим и решим систему уравнений:
2х+2у=50  2х+2у=50   48/у+2у=50     2у^2-50у+48=0     у^2-25у+24=0
ху=24       х=24/у        х=24/у            х=24/у                 х=24/у

у=24
х=1
Получим, что если х умножить на у будет 24*1=24.

Answer 2

P = 2*(Одна сторона + Вторая сторона)
50 = 2*(Одна сторона + Вторая сторона)
Одна сторона + Вторая сторона = 25
Одна сторона = 25 - Вторая сторона
или
Вторая сторона = 25 - Одна сторона
................................................
Площадь = Одна сторона * Вторую сторону
24 = (25 - Вторая сторона(Х))* Вторую сторону (Х)
24 = 25Х - X^2
-X^2 + 25X - 24 = 0
D = 625 - 4*(-1)*(-24) = 625 + 96 = 721
D > 0  ---> площадь этого прямоугольника может равняться 24 см^2

Answer 3

Finding the Length of a Rectangle Given the Perimeter

To find the length of a rectangle given its perimeter, you need to know the formula for the perimeter of a rectangle. The formula for the perimeter of a rectangle is:

Perimeter = 2 * (Length + Width)

In this case, the perimeter of the rectangle is given as 50 cm. Let's assume the length of the rectangle is represented by 'a' and the width is represented by 'b'. Using the formula above, we can set up the equation:

50 = 2 * (a + b)

Since we are trying to find the length of the rectangle, we need to express 'a' in terms of 'b' and the given perimeter. Let's solve for 'a':

50 = 2 * (a + b)

Divide both sides of the equation by 2:

25 = a + b

Subtract 'b' from both sides of the equation:

25 - b = a

Therefore, the length of the rectangle is equal to 25 - b.

Can the Area of the Rectangle be 24 cm²?

To determine if the area of the rectangle can be 24 cm², we need to use the formula for the area of a rectangle:

Area = Length * Width

Substituting the length expression we found earlier, we have:

Area = (25 - b) * b

Expanding the equation, we get:

Area = 25b - b²

To find out if the area can be 24 cm², we can set up the equation:

24 = 25b - b²

Rearranging the equation, we have:

b² - 25b + 24 = 0

We can solve this quadratic equation to find the possible values of 'b'. However, without additional information or constraints, we cannot determine if the area of the rectangle can be exactly 24 cm². It depends on the values of 'b' that satisfy the equation.

Please note that the given sources did not provide specific information about the area of the rectangle being equal to 24 cm².

Let me know if there's anything else I can help you with!