Question

Математика задача - 4/9 всей территории хозяйства занято лугом 3/7 части территории - пашней остальное лесом найти площадь всей территории и площадь леса если площадь луга больше площади пашни на 260 гектар

Answer 1

260*63=16380 4\9+3\7=55\ 63 63\63-55\63=8\63 16380*8\63= 2080 га.

Answer 2

Problem Analysis

We are given that 4/9 of the entire territory is occupied by meadows, 3/7 of the territory is occupied by arable land, and the rest is covered by forests. We need to find the total area of the territory and the area of the forest, given that the meadow is 260 hectares larger than the arable land.

Solution

Let's assume the total area of the territory is T hectares.

According to the problem, 4/9 of the territory is occupied by meadows, which is equal to (4/9) * T hectares.

Similarly, 3/7 of the territory is occupied by arable land, which is equal to (3/7) * T hectares.

The rest of the territory, which is covered by forests, can be calculated by subtracting the areas of meadows and arable land from the total area of the territory: Forest area = Total area - Meadow area - Arable land area

Given that the meadow area is 260 hectares larger than the arable land area, we can write the equation as: (4/9) * T = (3/7) * T + 260

Now, let's solve this equation to find the total area of the territory.

Calculation

To solve the equation, we can cross-multiply and simplify: (4/9) * T = (3/7) * T + 260

Multiply both sides of the equation by 63 (the least common multiple of 9 and 7) to eliminate the denominators: 28T = 27T + 16380

Subtract 27T from both sides of the equation: 28T - 27T = 16380 T = 16380

Therefore, the total area of the territory is 16380 hectares.

Now, let's calculate the area of the forest: Forest area = Total area - Meadow area - Arable land area Forest area = 16380 - (4/9) * 16380 - (3/7) * 16380

Using a calculator, we can simplify this expression: Forest area ≈ 16380 - 7280 - 7020 ≈ 2080 hectares

Therefore, the area of the forest is approximately 2080 hectares.

Answer

The total area of the territory is 16380 hectares and the area of the forest is approximately 2080 hectares.