Question

Площадь прямоугольника равна 14 см в квадрате,периметр-18см.найдите измерения прямоугольника.Дядя уехал если я не сделал он меня всего лешит он сказал.Помогите

Answer 1

Решаем систему уравнений:
(х+у)*2 = 18
х*у = 14

х+у = 9
х*у = 14

х = 9-у
(9-у)*у = 14
9у - у^2 = 14
у^2 - 9y + 14 = 0
По теореме Виета:
                     у1 = -7; у2= 2
-7 нам не подходит, т.к. длины отрицательными не бывают.
у = 2     х = 9 - 2 = 7
Ответ: длина прямоугольника 7 см,
            ширина прямоугольника 2 см.

Answer 2

Finding the Dimensions of a Rectangle

To find the dimensions of a rectangle given its area and perimeter, we can use a system of equations. Let's denote the length of the rectangle as L and the width as W.

Given that the area of the rectangle is 14 cm², we have the equation:

L * W = 14 Given that the perimeter of the rectangle is 18 cm, we have the equation:

2L + 2W = 18 We can solve this system of equations to find the values of L and W.

Solving the System of Equations

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

From equation 1, we can express L in terms of W:

L = 14 / W

Substituting this expression for L into equation 2, we get:

2(14 / W) + 2W = 18

Simplifying the equation:

28 / W + 2W = 18

Multiplying through by W to eliminate the fraction:

28 + 2W² = 18W

Rearranging the equation:

2W² - 18W + 28 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

W = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2, b = -18, and c = 28.

Plugging in the values:

W = (-(-18) ± √((-18)² - 4 * 2 * 28)) / (2 * 2)

Simplifying:

W = (18 ± √(324 - 224)) / 4

W = (18 ± √100) / 4

W = (18 ± 10) / 4

This gives us two possible values for W:

W₁ = (18 + 10) / 4 = 28 / 4 = 7

W₂ = (18 - 10) / 4 = 8 / 4 = 2

Now we can substitute these values of W back into equation 1 to find the corresponding values of L.

For W = 7:

L = 14 / 7 = 2

For W = 2:

L = 14 / 2 = 7

Therefore, the dimensions of the rectangle can be either 2 cm x 7 cm or 7 cm x 2 cm.

Conclusion

The dimensions of the rectangle can be either 2 cm x 7 cm or 7 cm x 2 cm.