Question

Периметр прямоугольника30 см.Найдите его стороны .площадь =36 см в квадрате

Answer 1

30:2=15 (сумма сторон)
а+в=15
а*в=36

пусть а ,будет у , а в будет х
у+х=15
у*х=36

у=15-х
(15-х)*х =36
15х-х^2=36

-х^2+15х-36=0
D=225-144= КОРЕНЬ ИЗ 81 =9
Х1= -15-9/-2 =12
Х2= -15+9/-2 =3

ответ : 12 и 3

Answer 2

Calculation of Rectangle Sides and Area

To find the sides of a rectangle with a perimeter of 30 cm and an area of 36 cm², we can use the following formulas:

1. Perimeter of a rectangle: P = 2(a + b), where a and b are the lengths of the sides. 2. Area of a rectangle: A = a * b, where a and b are the lengths of the sides.

Let's solve for the sides of the rectangle step by step:

1. Perimeter: - We are given that the perimeter is 30 cm, so we can write the equation as: 30 = 2(a + b). - Simplifying the equation, we have: 15 = a + b.

2. Area: - We are given that the area is 36 cm², so we can write the equation as: 36 = a * b.

Now, we have a system of equations: - Equation 1: 15 = a + b - Equation 2: 36 = a * b

To solve this system of equations, we can substitute the value of b from Equation 1 into Equation 2:

- Substitute b = 15 - a into Equation 2: 36 = a * (15 - a) - Simplify: 36 = 15a - a² - Rearrange the equation: a² - 15a + 36 = 0

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

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = -15, and c = 36, we can find the values of a and b.

Calculating the discriminant: D = b² - 4ac: - D = (-15)² - 4(1)(36) = 225 - 144 = 81

Since the discriminant is positive, we have two real solutions.

Using the quadratic formula: - a = (-(-15) ± √(81)) / (2(1)) - a = (15 ± 9) / 2

Solving for a: - a₁ = (15 + 9) / 2 = 24 / 2 = 12 - a₂ = (15 - 9) / 2 = 6 / 2 = 3

Now, we can substitute the values of a into Equation 1 to find the corresponding values of b:

- For a = 12: 15 = 12 + b => b = 15 - 12 = 3 - For a = 3: 15 = 3 + b => b = 15 - 3 = 12

Therefore, the sides of the rectangle are 12 cm and 3 cm.

To summarize: - The length of one side of the rectangle is 12 cm. - The length of the other side of the rectangle is 3 cm. - The area of the rectangle is 36 cm². - The perimeter of the rectangle is 30 cm.

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