A floor plan for the Mashaba Holdings offices is given below. The length of the building on the plan is 11.70 cm and the width is 10.41 cm. An electrical plan is also attached to the floor plan. Use the information on the floor plan to answer the following questions.

Here are the solutions to the questions:

4.1 Determine the number of telephone outlets in the building.

Step 1: Identify the symbol for a telephone outlet from the "ELECTRICAL PLAN" legend. It is a circle with a 'T' inside. Step 2: Count all instances of this symbol on the floor plan. • Boardroom: 2 outlets • Office 1 (top right): 1 outlet • Office 2 (bottom left): 1 outlet • Office 3 (middle left): 1 outlet • Office 4 (middle right): 1 outlet • Office 5 (bottom right): 1 outlet Total outlets = $2 + 1 + 1 + 1 + 1 + 1 = 7$

The number of telephone outlets is $\boxed{7}$.

4.2 Write down the ratio of the outside doors to the inside doors in simplest form.

Step 1: Count the outside doors. These are doors leading from the exterior into the building. • Main entrance (top left): 1 door • Boardroom entrance from outside (top left): 1 door Total outside doors = $1 + 1 = 2$ Step 2: Count the inside doors. These are doors connecting rooms within the building. • Boardroom to passage: 1 door • Passage to Office 1: 1 door • Passage to Office 2: 1 door • Passage to Office 3: 1 door • Passage to Office 4: 1 door • Passage to Office 5: 1 door Total inside doors = $1 + 1 + 1 + 1 + 1 + 1 = 6$ Step 3: Form the ratio and simplify. Ratio = Outside doors : Inside doors = $2 : 6$ Simplifying by dividing both sides by 2 gives $1 : 3$.

The ratio of outside doors to inside doors in simplest form is $\boxed{1:3}$.

4.3 Explain the meaning of the scale 1:200 on the plan.

The scale $1:200$ means that every unit of measurement on the plan represents $200$ of the same units in actual size. For example, $1 \text{ cm}$ on the plan corresponds to $200 \text{ cm}$ in reality.

4.4 Use the given scale to determine the actual dimensions of the building.

Step 1: Identify the given plan dimensions and the scale. Plan length = $11.70 \text{ cm}$ Plan width = $10.41 \text{ cm}$ Scale = $1:200$ Step 2: Calculate the actual length. Actual length = Plan length $\times$ Scale factor Actual length = $11.70 cm \times 200 = 2340 \text{ cm}$ Convert to meters: $2340 cm \div 100 = 23.40 \text{ m}$ Step 3: Calculate the actual width. Actual width = Plan width $\times$ Scale factor Actual width = $10.41 cm \times 200 = 2082 \text{ cm}$ Convert to meters: $2082 cm \div 100 = 20.82 \text{ m}$

The actual dimensions of the building are: Length: $\boxed{23.40 m}$ Width: $\boxed{20.82 m}$

4.5 The width of the building is 10.41cm. Verify if the width is correct. Show all calculations and write the answer in metres.

Step 1: The given plan width is $10.41 \text{ cm}$. The scale is $1:200$. Step 2: Calculate the actual width using the given plan width and scale. Actual width = Plan width $\times$ Scale factor Actual width = $10.41 cm \times 200 = 2082 \text{ cm}$ Step 3: Convert the actual width to metres. Actual width in metres = $2082 cm \div 100 = 20.82 \text{ m}$

The actual width of the building is $\boxed{20.82 m}$.

4.6 Determine the probability of finding a window on the eastern wall of the offices.

Step 1: Identify the eastern direction. According to the compass rose, East is to the right. Step 2: Identify the offices and their external eastern walls. • Boardroom (top left): Has no external eastern wall. • Office 1 (top right): Has an external eastern wall, and it contains a window. • Office 2 (bottom left): Has no external eastern wall. • Office 3 (middle left): Has no external eastern wall. • Office 4 (middle right): Has an external eastern wall, and it contains a window. • Office 5 (bottom right): Has an external eastern wall, and it contains a window. Step 3: Count the number of offices with an external eastern wall and the number of those walls that have windows. There are 3 distinct external eastern wall segments belonging to offices (Office 1, Office 4, Office 5). All 3 of these eastern wall segments have windows. Step 4: Calculate the probability. Probability = (Number of eastern office walls with windows) / (Total number of eastern office walls) Probability = $\frac{3}{3} = 1$

The probability of finding a window on the eastern wall of the offices is $\boxed{1}$.

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