This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the answers for Activity 6, Activity 7, and Activity 8. Activity 6: Budget-based fencing Given: Total available = R15 000 Labour cost = R2 000 Fencing cost = R130 per metre 1. How much money is available for fencing only? Step 1: Subtract the labour cost from the total available money. Money for fencing = Total available - Labour cost Money for fencing = R15\,000 - R2\,000 Money for fencing = R13\,000 The money available for fencing only is R13\,000. 2. Calculate the maximum perimeter that can be fenced. Step 1: Divide the money available for fencing by the cost per metre. Maximum perimeter = Money for fencingCost per metre Maximum perimeter = R13\,000R130/m Maximum perimeter = 100 m The maximum perimeter that can be fenced is 100 m. 3. Is it possible to fence a rectangular yard of 20 m × 15 m? Justify your answer. Step 1: Calculate the perimeter of the rectangular yard. Perimeter of yard = 2 × (length + width) Perimeter of yard = 2 × (20 m + 15 m) Perimeter of yard = 2 × (35 m) Perimeter of yard = 70 m Step 2: Compare the yard's perimeter with the maximum perimeter that can be fenced. Since 70 m < 100 m, it is possible to fence the yard. Yes, it is possible to fence a rectangular yard of 20 m × 15 m because its perimeter of 70 m is less than the maximum 100 m that can be fenced with the available budget. Activity 7: Identify the error Learner's calculation: Perimeter = 30 m × 20 m = 600 Cost = 600 × R120 = R72\,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 m^2 if it were area, or 100 m if it were perimeter). 2. Correct the calculation. Step 1: Calculate the correct perimeter for a rectangle with sides 30 m and 20 m. Correct Perimeter = 2 × (length + width) Correct Perimeter = 2 × (30 m + 20 m) Correct Perimeter = 2 × (50 m) Correct Perimeter = 100 m Step 2: Calculate the correct cost using the correct perimeter and the given cost per metre (R120). Correct Cost = Correct Perimeter × Cost per metre Correct Cost = 100 m × R120/m Correct Cost = R12\,000 The correct cost is R12\,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. That's 2 down. 3 left today — send the next one.