Question

Периметр поля прямоугольной форме равен 6 км,а его площадь 200 гектаров.Найдите длину и ширину поля.

Answer 1

1га=100 м*100 м=10000 м²
200 га=200*10000=2000000 м²
х м длина поля
у м ширина поля
Р=2(х+у)
2(х+у)=6000
S=x*y
x*y=2000000
 система:
{ x+y=3000         {x=3000-y
 x*y=2000000      (3000-y)*y=2000000
-y²+3000y-2000000=0
D=90000000-8000000=1000000=1000²
y₁=2000, y₂=1000
{x₁=1000           {x₂=2000
 y₁=2000            y₂=1000
ответ: размеры поля длина 2000 м, ширина 1000 м

Answer 2

Finding the Length and Width of a Rectangular Field

To find the length and width of a rectangular field given its perimeter and area, we can use the following formulas:

1. Perimeter of a rectangle: P = 2 * (length + width) 2. Area of a rectangle: A = length * width

In this case, we are given that the perimeter of the field is 6 km and its area is 200 hectares.

Let's solve for the length and width of the field step by step:

Step 1: Convert the area from hectares to square kilometers. - 1 hectare is equal to 0.01 square kilometers. - Therefore, the area of the field is 200 * 0.01 = 2 square kilometers.

Step 2: Set up the equations using the formulas mentioned above. - Perimeter equation: 6 = 2 * (length + width) - Area equation: 2 = length * width

Step 3: Solve the equations simultaneously to find the length and width. - We can rewrite the perimeter equation as: length + width = 3. - Rearranging the area equation, we get: length = 2 / width. - Substituting the value of length from the area equation into the perimeter equation, we have: 2 / width + width = 3. - Multiplying the equation by width to eliminate the fraction, we get: 2 + width^2 = 3 * width. - Rearranging the equation, we have: width^2 - 3 * width + 2 = 0. - Factoring the quadratic equation, we get: (width - 1) * (width - 2) = 0. - Therefore, the possible values for the width are 1 km and 2 km.

Step 4: Calculate the corresponding lengths. - If the width is 1 km, then the length is 2 / 1 = 2 km. - If the width is 2 km, then the length is 2 / 2 = 1 km.

Answer:

The length and width of the rectangular field can be either: - Length: 2 km, Width: 1 km - Length: 1 km, Width: 2 km

Please note that there may be other possible combinations of length and width that satisfy the given conditions, but these are the most straightforward solutions based on the information provided.