A rectangular paddock is of area 7 ha. One side is 600 m long. Then the other side in metres is?
Understand the Problem
The question is asking to find the length of one side of a rectangular paddock given its area in hectares and the length of the other side in meters. The approach would involve converting the area from hectares to square meters and then using the formula for the area of a rectangle (Area = length × width) to solve for the unknown side.
Answer
The other side in metres is approximately $116.67$ m.
Answer for screen readers
The length of the other side of the paddock is approximately (116.67) m.
Steps to Solve
- Convert Area from Hectares to Square Meters
To convert the area from hectares to square meters, use the conversion factor that (1 \text{ ha} = 10,000 \text{ m}^2). Therefore, for (7 \text{ ha}):
[ \text{Area in m}^2 = 7 \text{ ha} \times 10,000 \frac{\text{m}^2}{\text{ha}} = 70,000 \text{ m}^2 ]
- Use the Area Formula to Find the Unknown Side
The area of a rectangle is calculated using the formula:
[ \text{Area} = \text{length} \times \text{width} ]
Here, we have the area as (70,000 \text{ m}^2) and one side (length) as (600 \text{ m}). Let (w) be the width (the unknown side). Therefore, we can write:
[ 70,000 = 600 \times w ]
- Solve for the Width
To find (w), rearrange the equation:
[ w = \frac{70,000}{600} ]
Now, calculate the value:
[ w = \frac{70,000}{600} \approx 116.67 \text{ m} ]
The length of the other side of the paddock is approximately (116.67) m.
More Information
This calculation shows how to convert hectares to square meters and use the area formula for rectangles. The conversion factor is crucial when working with different units of measurement.
Tips
- Forgetting to convert hectares to square meters.
- Incorrectly applying the area formula by mixing up the terms (confusing length and width).
- Miscalculating during division.
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