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Sagot :
Certainly! Let's go through each part of the problem step by step.
### 1.2.1. Write the given scale in number scale format.
The scale given is 1 cm representing 1000 mm in real life. To write this in a number scale format, we first need to convert the units to be consistent.
1 centimeter (cm) is equivalent to 10 millimeters (mm). The scale states that 1 cm on the plan represents 1000 mm in real life. Since 1 cm = 10 mm, the scale can be converted to:
[tex]\[ \frac{10 \text{ mm}}{1000 \text{ mm}} = \frac{1}{100} \][/tex]
So, the number scale format is:
[tex]\[ 1:1000 \][/tex]
Thus, the scale in number scale format is 1:1000.
### 1.2.2. Measure the inner length of bedroom 2 and use the given scale to calculate the actual length (in m) of bedroom 2.
Assume the inner length of bedroom 2 measured on the plan is 5 cm.
Using the scale 1 cm = 1000 mm:
[tex]\[ \text{Actual length in real life (in mm)} = 5 \text{ cm} \times 1000 \text{ mm/cm} = 5000 \text{ mm} \][/tex]
Convert this value to meters (since 1000 mm = 1 m):
[tex]\[ \text{Actual length} = 5000 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} = 5 \text{ m} \][/tex]
So, the actual length of bedroom 2 is 5 meters.
### 1.2.3. Jan stated that the given scale is NOT very accurate to use if photocopies were going to be made of the plan. Critically comment on his statement and give a reason for your answer.
Jan's statement has merit. When photocopies are made of the plan, the scale may be altered because photocopy machines can introduce scaling errors. This means the dimensions on the photocopy may not be the same as the original plan's dimensions. Consequently, any measurements taken from the photocopy could be inaccurate if the copier does not maintain the original scale precisely. That's why it is essential to use the original plan or verify the scale post copying.
### Themba's garage is 3 m wide and 8 m long. Work out the length and width of the garage on a plan with the given scale.
Given measurements:
- Width = 3 meters
- Length = 8 meters
Using the scale 1:1000 (1 cm represents 1000 mm in real life):
First, convert meters to millimeters:
[tex]\[ \text{Width in mm} = 3 \text{ m} \times 1000 \text{ mm/m} = 3000 \text{ mm} \][/tex]
[tex]\[ \text{Length in mm} = 8 \text{ m} \times 1000 \text{ mm/m} = 8000 \text{ mm} \][/tex]
Now, convert these measurements from mm to the scale of the plan (1 cm = 1000 mm):
[tex]\[ \text{Width on plan (in cm)} = \frac{3000 \text{ mm}}{1000 \text{ mm/cm}} = 3 \text{ cm} \][/tex]
[tex]\[ \text{Length on plan (in cm)} = \frac{8000 \text{ mm}}{1000 \text{ mm/cm}} = 8 \text{ cm} \][/tex]
Therefore, on the plan, Themba's garage would be 3 cm wide and 8 cm long.
### 1.2.1. Write the given scale in number scale format.
The scale given is 1 cm representing 1000 mm in real life. To write this in a number scale format, we first need to convert the units to be consistent.
1 centimeter (cm) is equivalent to 10 millimeters (mm). The scale states that 1 cm on the plan represents 1000 mm in real life. Since 1 cm = 10 mm, the scale can be converted to:
[tex]\[ \frac{10 \text{ mm}}{1000 \text{ mm}} = \frac{1}{100} \][/tex]
So, the number scale format is:
[tex]\[ 1:1000 \][/tex]
Thus, the scale in number scale format is 1:1000.
### 1.2.2. Measure the inner length of bedroom 2 and use the given scale to calculate the actual length (in m) of bedroom 2.
Assume the inner length of bedroom 2 measured on the plan is 5 cm.
Using the scale 1 cm = 1000 mm:
[tex]\[ \text{Actual length in real life (in mm)} = 5 \text{ cm} \times 1000 \text{ mm/cm} = 5000 \text{ mm} \][/tex]
Convert this value to meters (since 1000 mm = 1 m):
[tex]\[ \text{Actual length} = 5000 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} = 5 \text{ m} \][/tex]
So, the actual length of bedroom 2 is 5 meters.
### 1.2.3. Jan stated that the given scale is NOT very accurate to use if photocopies were going to be made of the plan. Critically comment on his statement and give a reason for your answer.
Jan's statement has merit. When photocopies are made of the plan, the scale may be altered because photocopy machines can introduce scaling errors. This means the dimensions on the photocopy may not be the same as the original plan's dimensions. Consequently, any measurements taken from the photocopy could be inaccurate if the copier does not maintain the original scale precisely. That's why it is essential to use the original plan or verify the scale post copying.
### Themba's garage is 3 m wide and 8 m long. Work out the length and width of the garage on a plan with the given scale.
Given measurements:
- Width = 3 meters
- Length = 8 meters
Using the scale 1:1000 (1 cm represents 1000 mm in real life):
First, convert meters to millimeters:
[tex]\[ \text{Width in mm} = 3 \text{ m} \times 1000 \text{ mm/m} = 3000 \text{ mm} \][/tex]
[tex]\[ \text{Length in mm} = 8 \text{ m} \times 1000 \text{ mm/m} = 8000 \text{ mm} \][/tex]
Now, convert these measurements from mm to the scale of the plan (1 cm = 1000 mm):
[tex]\[ \text{Width on plan (in cm)} = \frac{3000 \text{ mm}}{1000 \text{ mm/cm}} = 3 \text{ cm} \][/tex]
[tex]\[ \text{Length on plan (in cm)} = \frac{8000 \text{ mm}}{1000 \text{ mm/cm}} = 8 \text{ cm} \][/tex]
Therefore, on the plan, Themba's garage would be 3 cm wide and 8 cm long.
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