Express the following scales as simplified ratios:
1 \text{ cm} represents 240 \text{ cm}.
1 \text{ cm} represents 2 \text{ km}.
3 \text{ cm} represents an actual distance of 9 \text{ m}.
5 \text{ cm} represents an actual distance of 30 \text{ km}.
60 \text{ mm} represents an actual distance of 5400 \text{ m}.
98 \text{ mm} represents an actual distance of 9.8 \text{ km}.
8\text{ mm} represents an actual distance of 40\text{ m}.
20\text{ cm} represents an actual distance of 16\text{ km}.
The walk from the roller coaster to the water slide is 450\text{ m}. The distance on the map between these two rides is 15\text{ cm}.
What is the actual distance from the roller coaster to the water slide in centimetres?
What ratio is the map using?
The owners of a treetop adventure park wish to connect two trees with a rope. The length between the two trees on a 1:400 map is 3\text{ cm}. What is the actual length between the two trees?
On a house plan that has been drawn to a scale of 1:100, the building is drawn to a length of 158\text{ mm}. Find the actual length of the building.
The scale on a map of a garden is 1:2000. The actual distance between the fountains is 100 metres.
What is the actual distance between the fountains in centimetres?
How far apart on the map should the two fountains be drawn?
A map has been drawn to a scale of 1:7000. Find, in metres, the actual distance between two points if the map distance between the points is 8\text{ mm}.
A school plans a 300\text{ m} race for students. The scale on a map of the school is 1:1000.
What is the actual race length in centimetres?
What length should the drawing of the race have on the school map?
The scale on a map is 1:25\,000. The actual distance between two buildings is 14\text{ km}.
What is the actual distance between the buildings in centimetres?
How far apart on the map should the two buildings be drawn 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}? Give your answer in centimetres.
A commercial plane measuring 66 metres long is to be represented on a scale model with a scale of 1:100. Find, in metres, the length of the plane in the scale model.
Given that the scale on a map is 1:25\,000, find the actual distance between two points which are drawn 14 \text{ cm} apart on the map in the following units:
Centimetres
Kilometres
A swimming pool of length 40\text{ m} and width 20\text{ m} is to be represented on a scale drawing with a scale of 1:2000.
Find the scaled length in centimetres.
Find the scaled width in centimetres.
On a map, 7\text{ cm} represents a distance of 63\text{ km}.
Write the scale as a ratio in simplified form.
Find the actual distance, in kilometres, represented on the map by 5\text{ cm}.
Find the distance on the map, in centimetres, that represents an actual distance of 54\text{ km}.
The scale of the map is 1:2000 and two points are drawn 19 \text{ cm} apart on the map. Find the actual distance between the points in metres.
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.
Find, in centimetres, the actual distance between two points which are drawn 12 \text{ cm} apart on that map.
Find the distance in metres between the two points from part (a).
Jimmy has a globe of the world that spins around so he can see where all of the countries that he wants to travel to are. The globe has a scale such that 1\text{ cm} on the globe represents a distance of 1000\text{ km} in real life.
State the scale ratio for this globe.
Consider the given floor plan:
According to the scale of the diagram, 1 \text{ cm} on the diagram represents how many metres in the house?
Using a ruler, Neville measures the length of Bed 1 on the plan and finds it to be 4 \text{ cm}. How many metres does this represent?
Using a ruler, Neville measures the width of Bed 1 on the plan and finds it to be 8 \text{ cm}. How many metres does this represent?
Neville wants to tile the floor of Bed 1. If each tile is 20 \text{ cm} by 10 \text{ cm}, how many tiles would Neville need?
If each tile weighs 200 \text{ g}, calculate the total weight of the tiles in grams.
Due to building regulations the total weight of the tiles cannot be more than 325 \text{ kg}. Convert your answer from part (e) to kilograms and determine if Neville will be able to use these tiles on the floor.
A scale model for a new skyscraper has been constructed and has model windows that are 1.54\text{ cm} wide. The actual windows will be 5.5\text{ m} wide.
Write the ratio of the scaled width to the actual width of the windows in the same units.
What ratio is the model using? Write your answer in simplest form.
The following is a 1:54\,000 scale drawing of the sailing route from the mainland to an island off the coast. The captain approximates the distance to be 15.6\text{ cm} on the map. What is the distance in kilometres of the boat trip?
According to the scale given on the map, estimate the actual distance from the mountain (triangle) to the house:
A map of a town is drawn to scale below:
Find the distance between house A and the park.
Find the distance between house C and the park.
Find the length of the shorter side of the park.
Find the length of the longer side of the park.
Find the distance between house A and house C, in kilometres, by travelling along the roads.
A map of a town is drawn to scale below:
Find the distance between house B and the park.
Find the distance between house D and the park.
Find the length of the shorter side of the park.
Find the distance between house B and house D, in kilometres, by travelling along the roads.
Koala airline has a simplified scale map of cities it flies between. What is the distance flown from Sydney to Brisbane?
Koala airlines has a simplified scale map of Australia which shows the cities it flies between. The the distance flown from Adelaide to Brisbane is 1600 \text{ km}.
Estimate the real distance the scale bar represents to the nearest 100 \text{ km}.
Nadia has just arrived in Bali for her holiday and is trying to work out how far apart certain places are to decide if she can walk between them or if she needs to catch a taxi.
She has checked-in to the Villa Nagal and wants to get a drink at De ja vu. According to the map, scale, and relevant symbols, find the approximate real-life distance between De ja Vu and Villa Nagal.
Using the scale provided on the map, find the approximate distance of the highlighted route:
The following picture represents the difference in width of human and Merino hair. The scale is one unit equals 0.005 \text{ mm}.
If the Merino hair on the diagram is 2 units wide, find its actual width.
The following picture is a scale drawing of a Tardigrade, a microscopic creature. The scale is one unit equals 0.03 \text{ mm}.
If the distance on the diagram from C to B is 8 units, find the actual distance from the top of the Taringrade's front shoulder to the top of its head.
The following is a 1:200 floor plan of a house. The homeowner wishes to add a dining room table, which is 250\text{ cm} long and placed where the \times is marked on the floor plan.
What length should the table be drawn to in the floor plans?
The floor plans for a double room and ensuite are given below.
What is the distance between the toilet and the ensuite door?
What is the distance between the shower and the toilet?
The dimensions of the triangle shown are enlarged using a scale factor of 3.1:
Find the new length of:
The dimensions of the triangle shown are reduced using a scale factor of 0.92:
Find the new length of:
AB
BC
CA
For the similar figures given, the scale factor used to enlarge the smaller quadrilateral is 4.5. Find the length of FG.
A circular oil spill has a radius of 20 metres. In a photo taken of the oil spill, the circle is reduced by a factor of 500. Find the radius of the circular oil spill in the photo, to the nearest centimetre.
A rectangle is 8\text{ cm} long and 6\text{ cm} wide. If its dimensions are enlarged such that the length is now 28\text{ cm}, find the new width.
If an image is enlarged by 250\%, what will be the scale factor?
Mae wants to insert a picture into a document. She enlarges it by a factor of 12 but it becomes too blurry, so she reduces the resulting picture by a scale factor of 4. Find the overall scale factor from the original to the final size.
A square with area 4 \text{ cm}^2 has its side lengths enlarged by a factor of 3.
What is the side length of the original square?
What will be the area of the new square?
By what factor has the area been enlarged?
A piece of sports tape in the shape of a rectangle measures 6\text{ cm} in width and 10\text{ cm} in length (when not stretched). When applied to Sophia’s shoulder, it is stretched so that it covers a rectangular area measuring 12\text{ cm} wide by 20\text{ cm} long.
When not stretched, what area does the tape cover?
When stretched, what area does the tape cover?
By what scale factor are the sides of the rectangular tape enlarged?
By what scale factor is the area of the rectangular tape enlarged?
An equilateral triangle of side length 6\text{ cm} is to be enlarged by a factor of 5.
What will be the side length of the resulting triangle?
What will be the size of each angle in the resulting triangle?
Find the value of x for each of the following pairs of similar shapes:
Consider the following similar figures:
Find the length scale factor from the left figure to the right figure.
Find the area scale factor from the left figure to the right figure.
Consider the following two triangles:
What scale factor is used to enlarge the small triangle?
What scale factor is used to reduce the large triangle?
What is the area of the small triangle?
What is the area of the large triangle?
What is the enlargement factor for the area of the small triangle?
A plan of a building with ratio 1:120 is enlarged so its length and width are both doubled.
What is the new scale ratio for the plans?
Is it accurate to use the original scale ratio for the new enlarged copy of the plan?
The scale bar on the original plan represents 6\text{ m}. When the plan is doubled, what length does the scale bar represent?
Can the scale bar be used for the new enlarged copy of the plan?