Math Problem Statement

The scale on a map is 1 : 50,000. If a road is 8 cm long on the map, how long is the road in real life? Give your answer in kilometres (km).

Solution

To solve this problem:

The scale on the map is 1 : 50,000, meaning that 1 cm on the map corresponds to 50,000 cm in real life.

  1. The road is 8 cm long on the map.

  2. Using the scale factor, we calculate the actual length of the road in real life:

Real length=8cm×50,000=400,000cm\text{Real length} = 8 \, \text{cm} \times 50,000 = 400,000 \, \text{cm}

  1. To convert 400,000 cm to kilometers, we use the fact that 100,000 cm = 1 km:

Real length=400,000100,000=4km\text{Real length} = \frac{400,000}{100,000} = 4 \, \text{km}

So, the real length of the road is 4 kilometers (km).

Would you like further details or clarifications?

Here are 5 related questions for practice:

  1. If a road is 10 cm long on a map with a scale of 1:50,000, what is the real length in kilometers?
  2. How long is a 5 cm road on a map with a 1:100,000 scale in real life?
  3. Convert 600,000 cm to kilometers.
  4. What is the real-life distance if a 12 cm line on the map is scaled at 1:25,000?
  5. How would you convert a road of 7 cm on a map at a scale of 1:20,000 to meters?

Tip: Always check units when converting distances, especially between cm and km!

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Math Problem Analysis

Mathematical Concepts

Scale Conversion
Unit Conversion

Formulas

Real length = Map length (cm) x Scale factor
Conversion from cm to km

Theorems

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Suitable Grade Level

Grades 7-9