Question

6. Периметр прямокутника 14 см, а його площа 10 см. Знайдіть сторони прямокутника, бистрої поможіть 14 б.​

Answer 1

Р = (a + b) · 2 = 14 см - периметр прямоугольника

a + b = 14 : 2 = 7 см - длина и ширина вместе

Пусть а = х см - длина, тогда b = (7 - х) см - ширина. Площадь прямоугольника 10 см². Уравнение:

х · (7 - х) = 10

7х - х² = 10

х² - 7х + 10 = 0

D = b² - 4ac = (-7)² - 4 · 1 · 10 = 49 - 40 = 9

√D = √9 = ±3

х = (-b±√D)/2a

х₁ = (7-3)/(2·1) = 4/2 = 2 см - длина

х₂ = (7+3)/(2·1) = 10/2 = 5 см - ширина

Ответ: 2 см и 5 см.

Answer 2

Problem Analysis

We are given the perimeter and area of a rectangle and we need to find the sides of the rectangle.

Solution

Let's assume the length of the rectangle is L and the width is W.

The perimeter of a rectangle is given by the formula: Perimeter = 2(L + W). Given that the perimeter is 14 cm, we can write the equation as: 2(L + W) = 14.

The area of a rectangle is given by the formula: Area = L * W. Given that the area is 10 cm², we can write the equation as: L * W = 10.

We have two equations with two variables. We can solve these equations simultaneously to find the values of L and W.

Solving the Equations

Let's solve the equations using substitution.

From the first equation, we can express L in terms of W as: L = (14 - 2W) / 2.

Substituting this value of L into the second equation, we get: (14 - 2W) / 2 * W = 10.

Simplifying the equation, we have: (14 - 2W) * W = 20.

Expanding and rearranging the equation, we get: 2W² - 14W + 20 = 0.

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

Using the quadratic formula, we have: W = (-b ± √(b² - 4ac)) / (2a).

Substituting the values of a, b, and c into the formula, we get: W = (-(-14) ± √((-14)² - 4 * 2 * 20)) / (2 * 2).

Simplifying the equation, we have: W = (14 ± √(196 - 160)) / 4.

Further simplifying, we get: W = (14 ± √36) / 4.

Taking the square root, we have: W = (14 ± 6) / 4.

So, we have two possible values for W: W₁ = (14 + 6) / 4 = 5 and W₂ = (14 - 6) / 4 = 2.

Now, we can substitute these values of W back into the equation L = (14 - 2W) / 2 to find the corresponding values of L.

For W = 5, we have: L = (14 - 2 * 5) / 2 = 2.

For W = 2, we have: L = (14 - 2 * 2) / 2 = 5.

Therefore, the sides of the rectangle are 2 cm and 5 cm.

Answer

The sides of the rectangle are 2 cm and 5 cm.