Question

Решите задачу методом проб и ошибок одна из сторон прямоугольника на 3 см длиннее другой а площадь этого прямоугольника равна 28 см2 найдите стороны и периметр этого прямоугольника​

Answer 1

Ответ:

Пошаговое объяснение:

Пусть одна сторона прямоугольника- х см, тогда вторая сторона (х-3)см. Составим уравнение:

х*(х-3) =28

x² - 3х - 28= 0

D= b²- 4ac= 3²- 4 *(-28)= 9 + 112= 121

√D= √121= 11

х=( -b±√D)/2а

х= (3+11)/2= 7 см одна сторона прямоугольника

х= (3-11)/2= -4 не является решением задачи

х-3= 7-3= 4 см вторая сторона прямоугольника

Answer 2

Problem Analysis

We are given that one side of a rectangle is 3 cm longer than the other side, and the area of the rectangle is 28 cm². We need to find the sides and perimeter of the rectangle.

Solution

Let's assume that the shorter side of the rectangle is x cm. Then the longer side will be (x + 3) cm.

The area of a rectangle is given by the formula: Area = length × width.

Given that the area is 28 cm², we can write the equation: x × (x + 3) = 28

To solve this equation, we can expand it: x² + 3x = 28

Rearranging the equation: x² + 3x - 28 = 0

Now we can solve this quadratic equation to find the value of x.

Solving the Quadratic Equation

To solve the quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 1, b = 3, and c = -28.

Substituting these values into the quadratic formula: x = (-3 ± √(3² - 4(1)(-28))) / (2(1))

Simplifying: x = (-3 ± √(9 + 112)) / 2 x = (-3 ± √121) / 2 x = (-3 ± 11) / 2

We have two possible solutions: 1. x = (-3 + 11) / 2 = 8 / 2 = 4 2. x = (-3 - 11) / 2 = -14 / 2 = -7

Since the length cannot be negative, we discard the second solution.

Therefore, the shorter side of the rectangle is 4 cm, and the longer side is (4 + 3) = 7 cm.

Calculating the Perimeter

The perimeter of a rectangle is given by the formula: Perimeter = 2 × (length + width).

Substituting the values we found: Perimeter = 2 × (4 + 7) = 2 × 11 = 22 cm

Answer

The sides of the rectangle are 4 cm and 7 cm, and the perimeter is 22 cm.