The scale on a map is $1 : 25000$ $1:25000$ .(A) find the distance in kilometres between two islands represented by a distance of $20 c m$ $20cm$ on the map. (B) find the distance between two towns on the map that are $10$ $10$ kilometres apart?

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Answer 1 · 2018-08-09T19:06:02

$(A) 5 k m$ $(A) 5 km$

$(B) 40 c m$ $(B) 40cm$

Direct proportion is an easy way of working with scales.

The ratio $1 : 25000$ $1 : 25000$ has no specific unit, but once a unit is chosen, the unit is the same for both.

Let's use $c m$ $cm$ because that is the unit used.

$1 c m : 25, 000 c m$ $1cm : 25,000cm$ means

$1 c m$ $1cm$ on the map represents :

$25, 000 \div 100, 000 = 0.25 k m$ $25,000 div 100,000 = 0.25 km$

Now you can compare $c m and k m$ $cm and km$

(A) $\frac{1}{0.25} = \frac{20}{x} \frac{\leftarrow c m}{\leftarrow k m}$ $1/0.25 = 20/x" "(larr cm)/(larr km)$

$x = 0.25 \times 20 = 5 k m$ $x = 0.25 xx20 = 5 km$

(B) $\frac{1}{0.25} = \frac{x}{10} \frac{\leftarrow c m}{\leftarrow k m}$ $1/0.25 = x/10" "(larr cm)/(larr km)$

$x = \frac{10}{0.25} = 40 c m$ $x = 10/0.25 = 40cm$

The scale on a map is 1:250001:25000 .(A) find the distance in kilometres between two islands represented by a distance of 20cm20cm on the map. (B) find the distance between two towns on the map that are 1010 kilometres apart?