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A football pitch measures 105 m by 68 m. A security fence is to be placed 4 m away from the edge of the pitch on all sides. Calculate the perimeter of the fence.

Mathematics

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Question 2.2.4

  1. Calculate the dimensions of the area enclosed by the fence.

    The pitch dimensions are 105 m105 \text{ m} by 68 m68 \text{ m}.
    The fence is placed 4 metres4 \text{ metres} away from the edge on all sides. This means the length and width of the fenced area will each increase by 4 m4 \text{ m} on both sides (total 8 m8 \text{ m}).

    Fenced length=105 m+(2×4 m)=105 m+8 m=113 m\text{Fenced length} = 105 \text{ m} + (2 \times 4 \text{ m}) = 105 \text{ m} + 8 \text{ m} = 113 \text{ m} Fenced width=68 m+(2×4 m)=68 m+8 m=76 m\text{Fenced width} = 68 \text{ m} + (2 \times 4 \text{ m}) = 68 \text{ m} + 8 \text{ m} = 76 \text{ m}
  2. Calculate the perimeter of the security fencing.

    The perimeter of a rectangle is given by P=2×(length+width)P = 2 \times (\text{length} + \text{width}).

    P=2×(113 m+76 m)P = 2 \times (113 \text{ m} + 76 \text{ m}) P=2×(189 m)P = 2 \times (189 \text{ m}) P=378 mP = 378 \text{ m}

    The total length (perimeter) of the security fencing required is 378 m\boxed{\text{378 m}}.

    Question 2.2.5

  3. Calculate the actual length of the West Club boundary line.

    The measured length on Annexure B is 42 mm42 \text{ mm}.
    The map scale is 1:12501 : 1250. This means 1 mm1 \text{ mm} on the map represents 1250 mm1250 \text{ mm} in reality.

    Actual length=Map length×Scale factor\text{Actual length} = \text{Map length} \times \text{Scale factor} Actual length=42 mm×1250=52500 mm\text{Actual length} = 42 \text{ mm} \times 1250 = 52500 \text{ mm}

    Convert the actual length to metres: 1 m=1000 mm1 \text{ m} = 1000 \text{ mm}.

    Actual length=52500 mm1000 mm/m=52.5 m\text{Actual length} = \frac{52500 \text{ mm}}{1000 \text{ mm/m}} = 52.5 \text{ m}
  4. Calculate the area of the boundary line.

    The boundary line is 0.1 m0.1 \text{ m} wide.

    Area of boundary line=Actual length×Width\text{Area of boundary line} = \text{Actual length} \times \text{Width} Area of boundary line=52.5 m×0.1 m=5.25 m2\text{Area of boundary line} = 52.5 \text{ m} \times 0.1 \text{ m} = 5.25 \text{ m}^2
  5. Calculate the total litres of paint needed.

    The specialized safety paint covers 5 m25 \text{ m}^2 per litre.

    Litres of paint needed=Area of boundary linePaint coverage per litre\text{Litres of paint needed} = \frac{\text{Area of boundary line}}{\text{Paint coverage per litre}} Litres of paint needed=5.25 m25 m2/litre=1.05 litres\text{Litres of paint needed} = \frac{5.25 \text{ m}^2}{5 \text{ m}^2/\text{litre}} = 1.05 \text{ litres}
  6. Calculate the number of paint tins needed.

    The paint is sold in 5-litre tins. Since you cannot buy a fraction of a tin, you must round up to the next whole number.

    Number of tins=⌈Litres of paint neededLitres per tin⌉\text{Number of tins} = \lceil \frac{\text{Litres of paint needed}}{\text{Litres per tin}} \rceil Number of tins=⌈1.05 litres5 litres/tin⌉=⌈0.21⌉=1 tin\text{Number of tins} = \lceil \frac{1.05 \text{ litres}}{5 \text{ litres/tin}} \rceil = \lceil 0.21 \rceil = 1 \text{ tin}
  7. Calculate the total cost of the paint tins.

    Each tin costs R849.50\text{R}849.50.

    Total cost=Number of tins×Cost per tin\text{Total cost} = \text{Number of tins} \times \text{Cost per tin} Total cost=1×R849.50=R849.50\text{Total cost} = 1 \times \text{R}849.50 = \text{R}849.50

    The total cost of the paint tins required to paint this boundary line is R849.50\boxed{\text{R}849.50}.

    Question 2.3.1

    This question requires "Annexure C (BMI Chart for Adults)" which is not provided in the image. Therefore, I cannot identify the specific BMI value for the spectator.

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