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Identify the given perimeter.

Mathematics

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3 parts
1.1

2019 m2019 \text{ m}

1.3

1122 poles1122 \text{ poles}

1.4

R93500.00

Step-by-step solution

6 steps

Here are the solutions to your questions, including corrections for 1.3 and 1.4 based on the correct pole spacing of 1.8 m1.8 \text{ m} from the image.

Part 1.1· 1 step

  1. Identify the given perimeter.

    The perimeter of the fence is indicated as 2019 m2019 \text{ m} in the problem statement.
    The final answer is 2019 m\boxed{2019 \text{ m}}.

    I noticed an error in my previous calculation for questions 1.3 and 1.4 due to misreading the pole spacing as 4.8 m4.8 \text{ m} instead of the correct 1.8 m1.8 \text{ m}. Here are the corrected solutions:

Part 1.3

1122 poles1122 \text{ poles}

(Corrected)

  1. Calculate the number of intervals for the 2019 m2019 \text{ m} fence with 1.8 m1.8 \text{ m} spacing.

    Number of intervals=Total lengthSpacing=2019 m1.8 m/interval=1121.666...\text{Number of intervals} = \frac{\text{Total length}}{\text{Spacing}} = \frac{2019 \text{ m}}{1.8 \text{ m/interval}} = 1121.666...
  2. Determine the number of poles.

    For a closed perimeter (like a fence around an area), the number of poles is equal to the number of intervals, rounded up to ensure full coverage.

    Number of poles=⌈1121.666...⌉=1122 poles\text{Number of poles} = \lceil 1121.666... \rceil = 1122 \text{ poles}

    The final answer is 1122 poles\boxed{1122 \text{ poles}}.

Part 1.4R93500.00

(Corrected)

  1. Calculate the cost if poles are bought in groups of 6 and individually for the remainder.

    Total poles needed: 1122.
    Number of groups of 6:

    Number of groups=11226=187\text{Number of groups} = \frac{1122}{6} = 187

    Since 1122 is perfectly divisible by 6, 187 groups of 6 poles will be bought, with no individual poles.
    Cost for groups: 187×R500=R93500187 \times R500 = R93500.
    Cost for individual poles: 0×R98.00=R0.000 \times R98.00 = R0.00.
    Total cost (groups + singles): R93500+R0.00=R93500.00R93500 + R0.00 = R93500.00.

  2. Calculate the cost if all poles are bought individually.

    Total cost (individually)=1122×R98.00=R109956.00\text{Total cost (individually)} = 1122 \times R98.00 = R109956.00
  3. Compare the costs.

    The cost of buying in groups (R93500.00R93500.00) is less than buying all individually (R109956.00R109956.00).
    The final answer is R93500.00\boxed{R93500.00}.

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