- Calculate the total area: \(12 \text{ hectares} = 120,000 \text{ } m^2\).
- Establish the area equation: \(l \times \omega = 120,000\).
- Define the length in terms of width: \(l = \frac{120,000}{\omega}\).
- Note that a unique solution requires more information; otherwise, the relationship is \(\boxed{l = \frac{120,000}{\omega}}\).
Explanation
- Calculate the total area in hectares
We are given a land restoration project where the seed rate is \(2.5 \text{ kg/hectare}\) and the total seed available is \(30 \text{ kg}\). To find the total area that can be seeded, we divide the total amount of seed by the seed rate per hectare.
\[\text{Total Area (in hectares)} = \frac{30 \text{ kg}}{2.5 \text{ kg/hectare}} = 12 \text{ hectares}.\]
- Convert the area to square meters
Knowing that \(1 \text{ hectare}\) is equivalent to \(10,000 \text{ square meters}\), we convert our total area from hectares into square meters:
\[\text{Total Area (in } m^2) = 12 \text{ hectares} \times 10,000 \text{ } m^2/\text{hectare} = 120,000 \text{ } m^2.\]
This represents the total area of the land to be restored.
- Form the equation and relate length and width
Let \(l\) represent the length of the land in meters and \(\omega\) represent the width of the land in meters. The area of a rectangular land is given by the product of its length and width:
\[l \times \omega = 120,000.\]
This equation shows the relationship between the length and the width for a given area of \(120,000 \text{ } m^2\). Since we have one equation with two unknown variables, the length and width cannot be uniquely determined without further information. However, we can express the length in terms of the width:
\[l = \frac{120,000}{\omega}.\]
For any given width \(\omega\), the corresponding length \(l\) is determined by this formula.
Examples
In agricultural planning, understanding the relationship between the dimensions of a plot and the resources needed is vital. For example, if you know the exact amount of fertilizer or seed available, you can determine the maximum area you can cultivate. By fixing one dimension (like the width of a path or the available equipment reach), you can calculate the necessary length for your planting beds to ensure all your resources are used efficiently without waste.