Question

Сумма длины и ширины прямоугольника равна 18 см. Чему равна площадь прямоугольника, если длина больше ширины на 4 см? 2 способа. Помогите пожалуйсто. Заранее спасибо без х!

Answer 1

Если бы длина была равна ширине, то их сумма была бы равна 18 - 4 = 14 см, тогда ширина равна 14:2 = 7 см. А длина 18 - 7 = 11 см. Значит, площадь прямоугольника, равная произведению длины и ширины, составит 7*11 = 77 кв. см.

Ответ: 77 кв. см.

Answer 2

х--ширина, х+4--длина

х+(х+4)=18

2х+4=18

2х=18-4

2х=14

х=14:2

х=7

7см--ширина,7+4=11длина,теперь ищем площадь

S=a*b

7*11=77кв.см.площадь прямоугольника.

Ответ: 77 кв.см.

без x нельзя,а других решений я не знаю(

Answer 3

Calculation of Rectangle's Area

To find the area of a rectangle, we need to know the length and width of the rectangle. In this case, we are given that the sum of the length and width of the rectangle is 18 cm, and the length is 4 cm greater than the width.

Let's denote the width of the rectangle as x cm. Since the length is 4 cm greater than the width, the length can be represented as x + 4 cm.

To find the area of the rectangle, we use the formula: Area = Length x Width.

Substituting the given values, we have:

Area = (x + 4) cm x x cm

Simplifying the expression, we get:

Area = x^2 + 4x cm^2

Now, we can proceed to find the area of the rectangle using two different methods.

Method 1: Using Quadratic Equation

We can solve the equation Area = x^2 + 4x by setting it equal to 18 cm (the sum of the length and width):

x^2 + 4x = 18

Rearranging the equation, we have:

x^2 + 4x - 18 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 4, and c = -18.

Substituting the values into the quadratic formula, we get:

x = (-4 ± √(4^2 - 4(1)(-18))) / (2(1))

Simplifying further, we have:

x = (-4 ± √(16 + 72)) / 2

x = (-4 ± √88) / 2

x = (-4 ± 2√22) / 2

Simplifying the expression, we get two possible values for x:

x = -2 + √22 or x = -2 - √22

Since the width cannot be negative, we discard the negative value and consider x = -2 + √22.

Now, we can substitute this value of x into the equation for the area:

Area = (-2 + √22)^2 + 4(-2 + √22)

Calculating the expression, we find that the area of the rectangle is approximately 22.49 cm^2.

Method 2: Using Factoring

Another way to find the area of the rectangle is by factoring the quadratic equation x^2 + 4x - 18 = 0.

We can rewrite the equation as:

x^2 + 6x - 2x - 18 = 0

Now, we can factor the equation:

x(x + 6) - 2(x + 6) = 0

Factoring out the common factor (x + 6), we have:

(x + 6)(x - 2) = 0

Setting each factor equal to zero, we get two possible values for x:

x + 6 = 0 or x - 2 = 0

Solving for x, we find:

x = -6 or x = 2

Since the width cannot be negative, we discard the negative value and consider x = 2.

Now, we can substitute this value of x into the equation for the area:

Area = (2 + 4)^2 + 4(2)

Calculating the expression, we find that the area of the rectangle is 36 cm^2.

To summarize, there are two possible values for the area of the rectangle: - Using the quadratic equation method, the area is approximately 22.49 cm^2. - Using the factoring method, the area is 36 cm^2.

Please note that the exact value of the area may depend on the precise measurements of the length and width of the rectangle.