Question

Периметр прямоугольника 22 см площадь 24 см как узнать длины

Answer 1

Пусть длина х см, ширина у см, тогда
2х+2у=22
х*у=24

х+у=11
х=11-у
(11-у)*у=24
11у-у²=24
у²-11у+24=0
у1=8   у2=3
х1=3   х2=8

Длина 8 см, ширина 3см, или наооброт длина 3 см, ширина 8 см.

Answer 2

Finding the Lengths of a Rectangle Given the Perimeter and Area

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

The perimeter of a rectangle is given by the formula: P = 2 * (a + b), where P is the perimeter and a and b are the lengths of the sides of the rectangle.

The area of a rectangle is given by the formula: A = a * b, where A is the area and a and b are the lengths of the sides of the rectangle.

In this case, we are given that the perimeter of the rectangle is 22 cm and the area is 24 cm². We need to find the lengths of the sides.

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

Solution:

Let's assume that a and b are the lengths of the sides of the rectangle.

From the given information, we have:

Perimeter (P) = 22 cm Area (A) = 24 cm²

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

Equation 1: P = 2 * (a + b) Equation 2: A = a * b

Substituting the given values into the equations, we have:

Equation 1: 22 = 2 * (a + b) Equation 2: 24 = a * b

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

From Equation 1, we can solve for a in terms of b:

a = (22 - 2b) / 2

Substituting this value of a into Equation 2, we have:

24 = [(22 - 2b) / 2] * b

Simplifying the equation, we get:

48 = 22b - 2b²

Rearranging the equation, we have:

2b² - 22b + 48 = 0

Now, we can solve this quadratic equation to find the values of b.

Using the quadratic formula, b = (-b ± √(b² - 4ac)) / (2a), where a = 2, b = -22, and c = 48, we can calculate the values of b.

After calculating the values of b, we can substitute them back into Equation 1 to find the corresponding values of a.

Let's calculate the values of a and b.

Using the quadratic formula, we find that b = 6 and b = 8.

Substituting these values back into Equation 1, we find that a = 5 and a = 3.

Therefore, the lengths of the sides of the rectangle are 5 cm and 3 cm.

Answer:

The lengths of the sides of the rectangle are 5 cm and 3 cm.