Sure, let's break down the problem step-by-step to find the correct solution:
### 1.1 Themba's Garage Dimensions on Different Scales
We start with the actual dimensions of Themba's garage, which are 3 meters for the width and 8 meters for the length. We need to convert these dimensions to various scales.
#### a) Scale 1:100
At a 1:100 scale, every 1 meter of the actual dimension is represented by 100 cm (since 1 meter = 100 cm).
- Width:
[tex]\[
3 \, \text{meters} \times 100 = 300 \, \text{cm}
\][/tex]
- Length:
[tex]\[
8 \, \text{meters} \times 100 = 800 \, \text{cm}
\][/tex]
#### b) Scale 1:200
At a 1:200 scale, every 1 meter of the actual dimension is represented by 200 cm (since 1 meter = 200 cm).
- Width:
[tex]\[
3 \, \text{meters} \times 200 = 600 \, \text{cm}
\][/tex]
- Length:
[tex]\[
8 \, \text{meters} \times 200 = 1600 \, \text{cm}
\][/tex]
#### c) Scale 1:50
At a 1:50 scale, every 1 meter of the actual dimension is represented by 50 cm (since 1 meter = 50 cm).
- Width:
[tex]\[
3 \, \text{meters} \times 50 = 150 \, \text{cm}
\][/tex]
- Length:
[tex]\[
8 \, \text{meters} \times 50 = 400 \, \text{cm}
\][/tex]
#### d) Scale 1:10
At a 1:10 scale, every 1 meter of the actual dimension is represented by 10 cm (since 1 meter = 10 cm).
- Width:
[tex]\[
3 \, \text{meters} \times 10 = 30 \, \text{cm}
\][/tex]
- Length:
[tex]\[
8 \, \text{meters} \times 10 = 80 \, \text{cm}
\][/tex]
### 1.2 Actual Dimensions of the Cupboard Floor
The plan of the cupboard has dimensions 2.5 cm by 3.6 cm and the scale is 1:50. To find the actual dimensions:
- Width:
[tex]\[
2.5 \, \text{cm} \times 50 = 125 \, \text{cm} = 1.25 \, \text{meters}
\][/tex]
- Length:
[tex]\[
3.6 \, \text{cm} \times 50 = 180 \, \text{cm} = 1.8 \, \text{meters}
\][/tex]
### 1.3 Scale of the Plan Representing 5 m by 25 cm
In this part, an actual length of 5 meters is represented by 25 cm on the plan. To determine the scale:
Convert 25 cm to meters:
[tex]\[
25 \, \text{cm} = 0.25 \, \text{meters}
\][/tex]
The scale factor would be the actual length divided by the plan length:
[tex]\[
\text{Scale factor} = \frac{5 \, \text{meters}}{0.25 \, \text{meters}} = 20
\][/tex]
Thus, the scale of the plan is 1:20.
### Final Answers Summary
1.1 Themba's garage scaled dimensions:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Scale} & \text{Width (cm)} & \text{Length (cm)} \\
\hline
1:100 & 300 & 800 \\
1:200 & 600 & 1600 \\
1:50 & 150 & 400 \\
1:10 & 30 & 80 \\
\hline
\end{tabular}
\][/tex]
1.2 Actual dimensions of the cupboard:
[tex]\[
1.25 \, \text{meters} \text{ by } 1.8 \, \text{meters}
\][/tex]
1.3 Scale of the plan:
[tex]\[
1:20
\][/tex]
