Question

По прямоугольному полю из одного угла в другой по диагонали проходит тропинка длиной  65 65 м. Найди площадь этого поля, если известно, что его длина на 23 23 м больше его ширины.

Answer 1

Ответ:1848

Объяснение:

Длина=x+23

По теореме Пифагора

c²=a²+b²

c⇒диагональ

а⇒ширина прямоугольника

b⇒длина прямоугольника

65²=x²+(x+23)²

1. x=-56

2. x=33

x=-56 не подходит, т.к значение стороны не может быть отрицательным

Ширина = 33

Длина=x+23= 56

Получаем

S=ab

S=33*56

S=1848

Answer 2

Calculation of the Area of the Rectangular Field

To find the area of the rectangular field, we need to determine the length and width of the field.

Let's assume the width of the field is x meters. According to the given information, the length of the field is 23 meters longer than its width. Therefore, the length of the field can be expressed as x + 23 meters.

We also know that a diagonal path passes through the field, which has a length of 65 meters.

To calculate the area of the field, we can use the formula for the area of a rectangle: Area = Length × Width.

Substituting the values we have:

Area = (x + 23) × x

Simplifying the equation:

Area = x^2 + 23x

Now, we need to solve for x to find the width of the field.

Solving for the Width of the Field

To find the width of the field, we can set up an equation using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the diagonal path in this case) is equal to the sum of the squares of the other two sides (the length and width of the field).

Using the Pythagorean theorem, we can set up the following equation:

x^2 + (x + 23)^2 = 65^2

Simplifying the equation:

x^2 + (x^2 + 46x + 529) = 4225

Combining like terms:

2x^2 + 46x + 529 = 4225

Rearranging the equation:

2x^2 + 46x - 3696 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = 46, and c = -3696.

After substituting the values into the quadratic formula and simplifying, we find two possible solutions for x: x = 32 or x = -58.5.

Since the width of the field cannot be negative, we discard the negative solution. Therefore, the width of the field is x = 32 meters.

Calculating the Area of the Field

Now that we know the width of the field is 32 meters, we can substitute this value back into the equation for the area of the field:

Area = (x + 23) × x = (32 + 23) × 32 = 55 × 32 = 1760 square meters

Therefore, the area of the rectangular field is 1760 square meters.

Please note that the calculations provided above are based on the given information and assumptions made.