Scales 2

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Scales 2

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Question 1 of 4

1. Question
An architect has designed a floor plan for a new bedroom with $1:80$ as the scale. If the length of the bedroom on the plan is $650 \text(mm)$ , what would the actual length be in metres?
- (52) $\text(m)$
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A scale is the ratio of the size of a model to the actual object it represents.

Quad boxes are used to easily find rates

First, fill up the quad boxes with the three known values and have the unknown value be $x$ .

Plan Actual

$1$ $80$

$650$ $x$

Next, equate the two columns and solve for $x$ .

$1/(650)$ $=$ $80/x$

$1(x)$ $=$ $80(650)$ Cross multiply

$x$ $=$ $52 000$

Since the given measurement for the plan is in $\text(mm)$ , this value will be $52 000 \text(mm)$ .

Finally, convert the millimetres into metres.

$1 \text(metre)$ $=$ $1000 \text(millimetres)$

$x$ $=$ $52 000xx1/(1000)$ $1000mm$ has $3$ zeroes $:.$ move $3$ decimal places to left

$x$ $=$ $(52 000)/(1000)$

$=$ $52$

$x=52 \text(m)$
Question 2 of 4

2. Question
A map indicates that the distance between two towns is $20\text(cm).$
If the scale of the map is $1:10 000$ , what is the actual distance between the two towns in kilometres?
- (2) $\text(km)$
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A scale is the ratio of the size of a model to the actual object it represents.

Quad boxes are used to easily find rates

First, fill up the quad boxes with the three known values and have the unknown value be $x$ .

Map Land

$1$ $10 000$

$20$ $x$

Next, equate the two columns and solve for $x$ .

$1/(20)$ $=$ $(10 000)/x$

$1(x)$ $=$ $10 000(20)$ Cross multiply

$x$ $=$ $200 000$

Since the given measurement for the map is in $\text(cm)$ , this value will be $200 000 \text(cm)$ .

Finally, convert the centimetres into kilometres.

$1 \text(kilometre)$ $=$ $100 000 \text(centimetres)$

$x$ $=$ $200 000xx1/(100 000)$ $100 000cm$ has $5$ zeroes $:.$ move $5$ decimal places to left

$x$ $=$ $(200 000)/(100 000)$

$=$ $2$

$x=2 \text(km)$
Question 3 of 4

3. Question
Complete the scale
- $1:100 000=1 \text(cm):$ (1) $\text(km)$
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A scale is the ratio of the size of a model to the actual object it represents.

First, complete the ratio on the right by using the same value and unit.

$1:$ $100 000$ $=$ $1$ $\text(cm)$ $:$ $100 000 \text(cm)$

Finally, convert the second ratio into kilometres.

$1 \text(kilometre)$ $=$ $100 000 \text(centimetres)$

$100 000xx(1)/(100 000)$ $=$ $1$

$1 \text(cm)$ $:$ $1 \text(km)$

$1 \text(km)$
Question 4 of 4

4. Question
Complete the scale
- $1:6000=1 \text(m):$ (6) $\text(km)$
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A scale is the ratio of the size of a model to the actual object it represents.

First, complete the ratio on the right by using the same value and unit.

$1:$ $6000$ $=$ $1$ $\text(m)$ $:$ $6000 \text(m)$

Finally, convert the second ratio into kilometres.

$1 \text(kilometre)$ $=$ $1000 \text(metres)$

$6000xx(1)/(1000)$ $=$ $6$

$1 \text(m)$ $:$ $6 \text(km)$

$6 \text(km)$

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Quizzes

$1/(650)$	$=$	$80/x$

$1(x)$	$=$	$80(650)$	Cross multiply
$x$	$=$	$52 000$

$x$	$=$	$52 000xx1/(1000)$	$1000mm$ has $3$ zeroes $:.$ move $3$ decimal places to left

$x$	$=$	$(52 000)/(1000)$

	$=$	$52$

$1/(20)$	$=$	$(10 000)/x$

$1(x)$	$=$	$10 000(20)$	Cross multiply
$x$	$=$	$200 000$

$x$	$=$	$200 000xx1/(100 000)$	$100 000cm$ has $5$ zeroes $:.$ move $5$ decimal places to left

$x$	$=$	$(200 000)/(100 000)$

	$=$	$2$

Plan	Actual
$1$	$80$
$650$	$x$

Map	Land
$1$	$10 000$
$20$	$x$

$100 000xx(1)/(100 000)$	$=$	$1$

$1 \text(cm)$	$:$	$1 \text(km)$

$6000xx(1)/(1000)$	$=$	$6$

$1 \text(m)$	$:$	$6 \text(km)$