A budget of R15,000 is available for fencing. Labour costs R2,000 and fencing costs R130 per metre. How much fencing can be purchased?

$$\text{Money for fencing} = \text{Total available} - \text{Labour cost}$$ $$\text{Money for fencing} = \text{R}15\,000 - \text{R}2\,000$$ $$\text{Money for fencing} = \text{R}13\,000$$

The money available for fencing only is $\boxed{\text{R}13\,000}$.

2. Calculate the maximum perimeter that can be fenced.

$$\text{Maximum perimeter} = \frac{\text{Money for fencing}}{\text{Cost per metre}}$$ $$\text{Maximum perimeter} = \frac{\text{R}13\,000}{\text{R}130/\text{m}}$$ $$\text{Maximum perimeter} = 100 \text{ m}$$

The maximum perimeter that can be fenced is $\boxed{100 \text{ m}}$.

3. Is it possible to fence a rectangular yard of $20 \text{ m} \times 15 \text{ m}$? Justify your answer.

$$\text{Perimeter of yard} = 2 \times (\text{length} + \text{width})$$ $$\text{Perimeter of yard} = 2 \times (20 \text{ m} + 15 \text{ m})$$ $$\text{Perimeter of yard} = 2 \times (35 \text{ m})$$ $$\text{Perimeter of yard} = 70 \text{ m}$$

Since $70 \text{ m} < 100 \text{ m}$, it is possible to fence the yard.
Yes, it is possible to fence a rectangular yard of $20 \text{ m} \times 15 \text{ m}$ because its perimeter of $70 \text{ m}$ is less than the maximum $100 \text{ m}$ that can be fenced with the available budget.

Activity 7: Identify the error
Learner's calculation:
Perimeter = $30 \text{ m} \times 20 \text{ m} = 600$
Cost = $600 \times \text{R}120 = \text{R}72\,000$

1. Identify two errors in the learner's method.

• The learner incorrectly calculated the perimeter by multiplying the length and width, which calculates the area, not the perimeter.
• The learner did not include the correct units for the perimeter calculation (it should be $600 \text{ m}^2$ if it were area, or $100 \text{ m}$ if it were perimeter).

2. Correct the calculation.

$$\text{Correct Perimeter} = 2 \times (\text{length} + \text{width})$$ $$\text{Correct Perimeter} = 2 \times (30 \text{ m} + 20 \text{ m})$$ $$\text{Correct Perimeter} = 2 \times (50 \text{ m})$$ $$\text{Correct Perimeter} = 100 \text{ m}$$

$$\text{Correct Cost} = \text{Correct Perimeter} \times \text{Cost per metre}$$ $$\text{Correct Cost} = 100 \text{ m} \times \text{R}120/\text{m}$$ $$\text{Correct Cost} = \text{R}12\,000$$

The correct cost is $\boxed{\text{R}12\,000}$.

3. Write a sentence explaining the correct method.
To calculate the cost of fencing, one must first find the perimeter of the area to be fenced, which is the total length of its boundary, and then multiply it by the cost per unit length.

Activity 8: Assessment-style reflection question
Explain why perimeter is used when calculating fencing costs but area is used when calculating paving costs.
Perimeter is used for fencing costs because fencing covers the boundary or outline of a space, which is a one-dimensional measurement of length. Area is used for paving costs because paving covers the entire surface or extent of a space, which is a two-dimensional measurement.