To determine the average gradient of the slope marked L-K, we need to understand how to calculate the gradient and what the options represent. The gradient is a measure of how steep a slope is, typically expressed as a ratio of vertical rise to horizontal run. Step-by-Step Explanation

1. Understanding Gradient:
2. The gradient is calculated using the formula: [ \text{Gradient} = \frac{\text{Vertical Rise}}{\text{Horizontal Run}} ]
3. This means for every unit of horizontal distance, how much vertical distance is gained.
4. Identifying Measurements:
5. To find the average gradient of the slope L-K, we need to measure the vertical rise (the change in elevation) and the horizontal run (the distance along the ground).
6. For example, if the slope rises 10 meters over a horizontal distance of 200 meters, the gradient would be: [ \text{Gradient} = \frac{10 \text{ m}}{200 \text{ m}} = \frac{1}{20} ]
7. This would be expressed as a ratio of 1:20.
8. Calculating the Gradient:
9. Suppose we have measured the vertical rise as 5 meters and the horizontal run as 100 meters. The calculation would be: [ \text{Gradient} = \frac{5 \text{ m}}{100 \text{ m}} = \frac{1}{20} ]
10. This means for every 20 meters horizontally, the slope rises 1 meter.
11. Interpreting the Options:
12. The options given are:
    • A. 1:15
    • B. 1:17
    • C. 1:19
    • D. 1:21
13. The correct option is C (1:19), which indicates that for every 19 meters of horizontal distance, the slope rises 1 meter.
14. Why Option C is Correct:
15. If the calculated gradient from the measurements taken on the slope L-K is approximately 1:19, it means that the slope is relatively gentle, as a higher number in the denominator indicates a less steep slope.
16. Why Other Options are Incorrect:
17. Option A (1:15): This indicates a steeper slope than 1:19. If the slope were 1:15, it would mean a rise of 1 meter for every 15 meters horizontally, which is steeper than what we have calculated.
18. Option B (1:17): Similar to option A, this also suggests a steeper slope than 1:19. It would indicate a rise of 1 meter for every 17 meters horizontally.
19. Option D (1:21): This indicates a gentler slope than 1:19. A gradient of 1:21 would mean a rise of 1 meter for every 21 meters horizontally, which is less steep than what we have calculated.

Common Pitfalls

• Misreading Measurements: Ensure that the vertical rise and horizontal run are accurately measured. A small error in measurement can lead to a significant difference in the calculated gradient.
• Confusing Ratios: Remember that a higher denominator in the ratio indicates a gentler slope, while a lower denominator indicates a steeper slope.
• Units Consistency: Always ensure that the units for vertical rise and horizontal run are the same (e.g., both in meters) to avoid calculation errors.

Revision Summary

• The average gradient is calculated as the ratio of vertical rise to horizontal run.
• The correct answer for the slope L-K is C (1:19), indicating a moderate slope.
• Other options (A, B, D) represent steeper or gentler slopes than the calculated gradient.
• Accurate measurement and understanding of ratios are crucial for gradient calculations.