14.05 Maps and scale

Convert the following descriptions to a scale ratio:

The scale on a map of a garden is 1:2000. How far apart on the map should two fountains be drawn if the actual distance between the fountains is 100 \text{ m}? Express your answer in centimetres.

The scale on a map is 1:400\,000. How far apart on the map should two train stations be drawn if the actual distance between the stations is 100 \text{ km}? Express your answer in centimetres.

Consider a map with a scale of 1:2000.

Consider a map with a scale of 1:25\,000.

Bianca is looking over a map of her local area and notices that the scale of the map is given as 1:100 in the map legend.

Below is a map of New York. The actual dimensions of one rectangular block is 230 \,\text{m} by 80 \,\text{m}.

Use the map below to find the distance between Adelaide and Brisbane:

This is a map of where Adam and Carl live. The side of a small square on the map represents 100 \,\text{m}:

Adam is on the corner of Top Lane and Major Street (map reference E 5). He walks 300\text{ m} along Top Lane to Carl's house.

Write the map reference of Carl's house.

The map designer for a new amusement park measures the main street to be 4 \, \text{cm}. The walk along the main street is actually 120 \,\text{m}:

Write down the scale ratio of the map.

A map of a town is drawn to scale below:

Estimate the distance from Perth to Brisbane using the map scale:

The scale on the map of a public garden is 1:5000. How far apart on the map should two ponds be if the actual distance between the ponds is 350\text{ m}? Give your answer in centimetres.

Vincent is comparing three parks from three different maps shown below. Which park has the largest area? Explain your answer.

Lesse park

Scale: 1:2000

Millenial park

Scale: 1:5000

Tibsen park

Scale: 1:7000

A map is being drawn for a medium-sized rural town. The map will fit on an A4 piece of paper which has the dimension of 21\,\text{cm} by 29.7\,\text{cm}. Write an appropriate scale for the map.

An oil tanker has a spill off the coast of Australia. An expert says that the oil could travel 1700\text{ km} in the first day. Their map is shown sketched with circles with radius 10\, \text{cm}, 20 \, \text{cm} and 30 \, \text{cm}:

The following is a 1:200 floor plan of a house. The homeowner wishes to add a dining room table, which is 150\text{ cm} long, placing it where the \times is marked on the floor plan.

Find the table's length that should be drawn to in the floor plans.

A plan of a building with ratio 1:90 is enlarged so its length and width are both doubled as shown:

An architect is designing a house that is 21 \, \text{m} long and 15 \,\text{m} wide.