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WAEC Mathematics 2016 Paper

Question : 6

Total: 49

On a map, 1cm represent 5km. Find the area on the map that represents 100km².

Solution:

Concept:

When scale is given in linear units, the area ratio is the square of the linear scale ratio. So

1

cm on the map represents

5

km on the ground, meaning

1 \text{ cm}^2

represents

(5 \text{ km})^2 = 25 \text{ km}^2

Explanation:

Let the required map area be

x \text{ cm}^2

Since

1 \text{ cm}^2

represents

25 \text{ km}^2

, the ratio is:

\frac{x \text{ cm}^2}{100 \text{ km}^2} = \frac{1 \text{ cm}^2}{25 \text{ km}^2}

Cross-multiply to get:

x = \frac{100}{25}

x = 4 \text{ cm}^2

Thus, the area on the map that represents

100 \text{ km}^2

4 \text{ cm}^2

Answer:

4 \text{ cm}^2

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