Tag: changing scale

Questions Related to changing scale

On a scale map $0.7\ cm$ represents $8.4\ km$. If the distance between two points on the map is $46.5\ cm$, what is the actual distance between the points?

maths bearing and drawings mapping mapping space around us changing scale

  1. $56\ km$

  2. $55.80\ km$

  3. $62.80\ km$

  4. $72\ km$

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Correct Option: B
Explanation:

Given $0.7$cm represents $8.4$ km 

$46.5$ cm represents $x$
By proportionality 

$\dfrac{0.7}{46.5} = \dfrac{8.4}{x}$

$x = \dfrac{8.4\times46.5}{0.7}$
 
$x = 55.80km$

The perimeter of two similar triangles $ABC$ and $PQR$ are $36\ cm$ and $24\ cm$ respectively. If $PQ = 10\ cm$ then the length of $AB$ is

maths bearing and drawings mapping mapping space around us changing scale

  1. $18\ cm$

  2. $12\ cm$

  3. $15\ cm$

  4. $30\ cm$

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Correct Option: C
Explanation:

$\triangle ABC = \triangle PQR$, then
$\dfrac {\text {Perimeter of}\triangle ABC}{\text {Perimeter of}\triangle PQR} = \dfrac {AB}{PQ} = \dfrac {BC}{QR} = \dfrac {AC}{PR}$
$\dfrac {36}{24} = \dfrac {AB}{10}; AB = \dfrac {36}{24}\times 10 = 15\ cm$.