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A wall has a total length of 5.48 meters. It has two garage doors, each 2.44 meters wide and 2.1 meters high. There are also two side wall sections, each 0.15 meters wide. Calculate the area of the wa

Mathematics

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4 steps
  1. Determine the length and width of one garage door in meters.

    From the diagram:
    The length (height) of one garage door is 2100 mm2100 \text{ mm}.
    The width of one garage door is 2440 mm2440 \text{ mm}.
    To convert millimeters to meters, we divide by 1000.

    Length=2100 mm1000 mm/m=2.100 m\text{Length} = \frac{2100 \text{ mm}}{1000 \text{ mm/m}} = 2.100 \text{ m} Width=2440 mm1000 mm/m=2.440 m\text{Width} = \frac{2440 \text{ mm}}{1000 \text{ mm/m}} = 2.440 \text{ m}

    The length of one garage door is 2.100 m\boxed{\text{2.100 m}} and the width is 2.440 m\boxed{\text{2.440 m}}.

  2. Calculate A, the length of the wall between the two garage doors, in mm.

    The total length of the wall is given as 5480 mm5480 \text{ mm}.
    The diagram shows two side wall sections, each 150 mm150 \text{ mm} wide.
    The diagram shows two garage doors, each 2440 mm2440 \text{ mm} wide.
    The total length of the wall is the sum of the two side wall sections, the two garage door widths, and the length A between the doors.

    5480 mm=(2×150 mm)+(2×2440 mm)+A5480 \text{ mm} = (2 \times 150 \text{ mm}) + (2 \times 2440 \text{ mm}) + A 5480 mm=300 mm+4880 mm+A5480 \text{ mm} = 300 \text{ mm} + 4880 \text{ mm} + A 5480 mm=5180 mm+A5480 \text{ mm} = 5180 \text{ mm} + A A=5480 mm−5180 mmA = 5480 \text{ mm} - 5180 \text{ mm} A=300 mmA = 300 \text{ mm}

    The length of A is 300 mm\boxed{\text{300 mm}}.

  3. Determine the total area of the two garage doors.

    The area of one garage door is its length (height) multiplied by its width.
    Length of one garage door = 2100 mm2100 \text{ mm}
    Width of one garage door = 2440 mm2440 \text{ mm}

    Area of one garage door=2100 mm×2440 mm=5124000 mm2\text{Area of one garage door} = 2100 \text{ mm} \times 2440 \text{ mm} = 5124000 \text{ mm}^2

    The total area of the two garage doors is twice the area of one garage door.

    Total area of two garage doors=2×5124000 mm2=10248000 mm2\text{Total area of two garage doors} = 2 \times 5124000 \text{ mm}^2 = 10248000 \text{ mm}^2

    The total area of the two garage doors is 10248000 mm2\boxed{\text{10248000 mm}^2}.

  4. Calculate the total area of the part of the wall that consists of bricks if B is 1.5 times the length of A.

    Give your answer in m².
    First, calculate B.

    B=1.5×AB = 1.5 \times A

    From Step 2, $

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