Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 5: Exercise 2

A map has a scale of $1:10000$. The distance between two villages on the map is $25 \mathrm{cm}$. What is the actual distance between the village in $\mathrm{km}$?

A map has a scale of $1:10000$. The length of the road from the church to the top of the hill is $800 \mathrm{m}$. What length, in $\mathrm{cm}$, on the map represents the road?

The diagram (not drawn to scale) shows a park which is $500 \mathrm{m}$ long and $600 \mathrm{m}$ wide. It has a triangular play area in one corner which has one side of $200 \mathrm{m}$ and another side of $300 \mathrm{m}$ as shown in the diagram. At the other end of the park there is a small rectangular park of $200 \mathrm{m}$ long and $100 \mathrm{m}$ wide.

Make a scale drawing of the park and its features using a scale of $2 \mathrm{cm}$ to represent $100 \mathrm{m}$.

The diagram (not drawn to scale) shows a park which is $500 \mathrm{m}$ long and $600 \mathrm{m}$ wide. It has a triangular play area in one corner which has one side of $200 \mathrm{m}$ and another side of $300 \mathrm{m}$ as shown in the diagram. At the other end of the park there is a small rectangular park of $200 \mathrm{m}$ long and $100 \mathrm{m}$ wide.

Make a scale drawing of the park and its features using a scale of $2 \mathrm{cm}$ to represent $100 \mathrm{m}$. What is the shortest distance between the play area and the car park on the scale drawing?

Peta makes a scale drawing of the floor plan of her bedroom. Her actual measurements are correct but one of the measurements of her scale drawing is incorrect. The table shows her measurements.

Which one of the measurement is incorrect? Give reasons for your answer.

A map is drawn using a scale of $2 \mathrm{cm}$ to represent $250 \mathrm{m}$. This can also be written as a scale of $1:$ _____

The diagram is a map showing two towns $\mathrm{A}$ and $\mathrm{B}$. This map is drawn to a scale of $1 \mathrm{cm}$ represents $2 \mathrm{km}$. $\mathrm{B}$ is due west of $\mathrm{A}$.

How far is $\mathrm{A}$ from $\mathrm{B}$ in real life?

The diagram is a map showing two towns $\mathrm{A}$ and $\mathrm{B}$. This map is drawn to a scale of $1 \mathrm{cm}$ represents $2 \mathrm{km}$. $\mathrm{B}$ is due west of $\mathrm{A}$.

Town $\mathrm{C}$ is on a bearing of $070°$ from $\mathrm{A}$ and $290°$ from $\mathrm{B}$. Mark the position of $\mathrm{C}$ onto your scale drawing.