Sec 3 · G1 (N(T))

Congruence and similarity

Practise congruence and similarity with step-by-step help. Free account.

1. Scale drawings and maps

Units
$1$ m	$100$ cm
$1$ km	$1000$ m $= 100\,000$ cm

Scale	With units	Simplest
$1 : 50\,000$	$1$ cm $: 50\,000$ cm	$1$ cm $: 0.5$ km
$1 : 200$	$1$ cm $: 200$ cm	$1$ cm $: 2$ m

Map to actual: 2.4 cm on a 1 : 50 000 map

\displaystyle 1\text{ cm} : 0.5\text{ km}

Find the scale: 2 cm for 1 km

\displaystyle 2\text{ cm} : 1\text{ km}

📖 Worked example

A map is drawn to a scale of $1 : 50\,000$ . Two towns are $2.4$ cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Step 1 of 2

Write the scale as a ratio with units (1 km = 100 000 cm)

\mathstrut 1 : 50\,000

\mathstrut 1\text{ cm} : 50\,000\text{ cm}

1\text{ cm} : 0.5\text{ km}

📖 Worked example

Two towns are $1$ km apart. On a map they are $2$ cm apart. Express the scale of the map in the form $1 : n$ .

Step 1 of 3

Write map : actual with units

\mathstrut 2\text{ cm} : 1\text{ km}

Practise congruence and similarity with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

1. Scale drawings and maps

Units
$1$ m	$100$ cm
$1$ km	$1000$ m $= 100\,000$ cm

Scale	With units	Simplest
$1 : 50\,000$	$1$ cm $: 50\,000$ cm	$1$ cm $: 0.5$ km
$1 : 200$	$1$ cm $: 200$ cm	$1$ cm $: 2$ m

Map to actual: 2.4 cm on a 1 : 50 000 map

\displaystyle 1\text{ cm} : 0.5\text{ km}

Find the scale: 2 cm for 1 km

\displaystyle 2\text{ cm} : 1\text{ km}

📖 Worked example

A map is drawn to a scale of $1 : 50\,000$ . Two towns are $2.4$ cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Step 1 of 2

Write the scale as a ratio with units (1 km = 100 000 cm)

\mathstrut 1 : 50\,000

\mathstrut 1\text{ cm} : 50\,000\text{ cm}

1\text{ cm} : 0.5\text{ km}

📖 Worked example

Two towns are $1$ km apart. On a map they are $2$ cm apart. Express the scale of the map in the form $1 : n$ .

Step 1 of 3

Write map : actual with units

\mathstrut 2\text{ cm} : 1\text{ km}

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