Question

Реши задачу с помощью уравнения. Длина прямоугольника на 7 см больше ширины, а его площадь равна 60 см². Найди стороны прямоугольника и его периметр. СПОЧНО!!

Answer 1

Ответ:

Объяснение:

1) Пусть длинна прямоугольника = (х+7) см, а ширина = (х) см

за формулой площади S=a*b имеем уравнение:

х+7*х=60

2х+7=60

2х=60-7

2х=53

х= 26,5 см - ширина

длинна = 7+26,5=33,5

P=a+b

P=33,5+26,5=60

Answer 2

Problem Analysis

We are given that the length of a rectangle is 7 cm greater than its width, and the area of the rectangle is 60 cm². We need to find the dimensions of the rectangle and its perimeter.

Solution

Let's assume the width of the rectangle is x cm. According to the problem, the length of the rectangle is 7 cm greater than its width, so the length would be x + 7 cm.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 60 cm². We can set up the equation as follows:

x(x + 7) = 60

To solve this equation, we can expand it and rearrange it into a quadratic equation:

x² + 7x - 60 = 0

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

Solving the Quadratic Equation

We can solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 1, b = 7, and c = -60.

Substituting these values into the quadratic formula, we get:

x = (-7 ± √(7² - 4(1)(-60))) / (2(1))

Simplifying further:

x = (-7 ± √(49 + 240)) / 2

x = (-7 ± √289) / 2

x = (-7 ± 17) / 2

So we have two possible solutions for x:

1. x = (-7 + 17) / 2 = 5 2. x = (-7 - 17) / 2 = -12

Since the width of a rectangle cannot be negative, we discard the second solution.

Therefore, the width of the rectangle is 5 cm.

To find the length, we can substitute this value back into the equation: Length = Width + 7.

Length = 5 + 7 = 12 cm

So the dimensions of the rectangle are 5 cm (width) and 12 cm (length).

Calculating the Perimeter

The perimeter of a rectangle is given by the formula: Perimeter = 2(Length + Width).

Substituting the values we found, we get:

Perimeter = 2(12 + 5) = 2(17) = 34 cm

Therefore, the perimeter of the rectangle is 34 cm.

Conclusion

The width of the rectangle is 5 cm, the length is 12 cm, and the perimeter is 34 cm.