A street guide for Belfast has a scale of 1:15 000. A walkway through the city is 2.4 km long. Find the length of the walkway on the map. Give your answer in centimetres.
Let's use a proportion.
1/15,000 = x/2.4
15,000x = 2.4
x = 2.4/15,000
x = 0.00016 km = ?? cm
16cm
To find the length of the walkway on the map, we need to use the scale provided on the street guide. The scale given is 1:15,000, which means that 1 unit on the map represents 15,000 units in real life.
Given that the walkway in real life is 2.4 km long, we can find the length of the walkway on the map by setting up a proportion.
Let's represent the length of the walkway on the map as x centimeters.
Using the given scale, we know that 1 cm on the map represents 15,000 cm in real life. Therefore, we can write the proportion:
1 cm on map / 15,000 cm in real life = x cm on map / 2.4 km in real life
First, let's convert 2.4 km to centimeters. Since there are 1,000 meters in a kilometer and 100 centimeters in a meter, we can calculate:
2.4 km = 2.4 x 1,000 x 100 = 240,000 cm
Plugging this value into the proportion, we have:
1 cm / 15,000 cm = x cm / 240,000 cm
To solve for x, we can cross multiply:
15,000 cm * x cm = 1 cm * 240,000 cm
15,000x = 240,000
Now, divide both sides of the equation by 15,000 to solve for x:
x = 240,000 / 15,000
x ≈ 16 cm
Therefore, the length of the walkway on the map is approximately 16 centimeters.