Enlargement
2
Scale and Enlargement
Here is a picture of Andy.
He is 7·5 cm tall in the picture.
In real life, Andy is actually twenty times the size
he appears to be in the picture.
We say that this picture has “a scale of 1 cm to 20 cm”,
which tells us that the “real life” Andy is twenty times
the size of the one which we see here in the picture.
(i.e. 20 x 7·5 = 150 cm)
Exercise 1
1.
Here are some “scales”.
What number would you have to multiply any measurement by to arrive at the
“real life” size ?
2.
a
1 cm to 8 cm
b
1 m to 100 m
c
1 m to 6 m
d
1 cm to 1 metre
e
1 : 9 (“one to nine”)
f
1 : 100.
More “scales”.
You would have to divide any real length by the scale number to reduce the “real life”
situation into a “model” or “photograph” situation.
What would you divide by here to reduce the “real life” to the “model” situation :–
3.
a
1 cm to 10 cm
b
1 m to 50 m
c
1:5
d
1 : 30
e
1 m to 10 km
f
1 mm to 2 cm.
careful
Use a ruler to measure these lines and use the given scales to find the “real life”
distance the lines represent :–
a
Scale 1 cm to 10 cm (length x 10)
b
Scale 1 cm to 100 cm
c
Scale 1 : 10
d
Scale 1 : 100
e
Scale 1 cm to 1 m
f
Scale 1 cm to 1 km.
National 4 Book N4-1
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Chapter 21 - Enlargement 2
4.
This model car was made to a scale of 1 cm to 50 cm.
..... cm
5.
a
Measure the length of the car in the drawing above.
b
Use the scale (1 cm = 50 cm) to find the length of the real car.
The model bus is made to the scale of 1 cm to 80 cm.
a
Measure the height of the bus.
b
Calculate the height of the real bus.
..... cm
6.
The flagpole has a scale of 1 cm to 120 cm.
a
Measure the height of the flagpole.
b
Calculate its real height.
..... cm
National 4 Book N4-1
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Chapter 21 - Enlargement 2
The side of each small square represents 50 cm in this scale drawing of a greenhouse.
POTS
WORK
BENCH
BEDDING
PLANTS
X
Y
TOMATOES
7.
LETTUCE
50 cm
50 cm
a
b
Calculate the real length of :–
(i)
the row of pots.
(ii)
the row of tomatoes.
(iii)
the trays of lettuce.
(iv)
the trays of bedding plants.
The gardener walks in a straight line from his work bench (X) to the tomatoes (Y).
How far did he really walk ?
Calculating Lengths using Scales and Scale Factors
Example :–
A model van is 8 centimetres long.
The scale of the model is 1 : 50.
(This means that the scale factor for the question is 50).
Calculate the real length of the van.
Solution :-
Real length of van = 50 x model length
= 50 x 8 cm
= 400 cm (or 4 metres)
Exercise 2
1.
Calculate the real lengths of these models, given their model lengths
and their scale factors :–
a
A model bus, length 10 cm.
(Scale factor 50).
b
A model ship, length 20 cm.
(Scale factor 100).
c
A model steam engine, length 5 cm. (Scale factor 200).
d
A model aeroplane, length 12 cm.
National 4 Book N4-1
(Scale factor 250).
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Chapter 21 - Enlargement 2
2.
A photograph shows that Charlie is 15 cm tall.
The scale of the drawing is 1 : 10.
What is Charlie’s real height ?
3.
Mary’s foot is TWICE the length of her baby sister’s.
Her sister’s foot is 8·8 centimetres long.
a
Write down the scale factor here.
b
What size are Mary’s feet ?
4.
Harold has drawn up a plan of his rectangular garden.
The drawing is 15 centimetres long and 10 centimetres wide.
The scale of his garden on the map is given as 1 : 50.
a
Write down the scale factor.
b
(i)
Calculate the length of the actual garden.
(ii)
Calculate the width of the actual garden.
Calculating Model Lengths knowing Scale Factor
Example :–
A van is 400 cm long.
A model of this van is made 50 times
smaller than the actual van.
Find the length of the model.
(This time, though the scale is still 1 : 50, the scale factor is
—>
Solution :-
).
This will reduce the length of the real van !!!
Length of model
=
1
x
50
real length
=
1
x
50
400 cm (= 400 ÷ 50)
=
National 4 Book N4-1
1
50
8 cm
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Chapter 21 - Enlargement 2
5.
Calculate the heights of these models, given their real heights and scale factors :–
a
A van 150 cm high.
(Scale factor
1
50
)
b
A lorry 300 cm high.
(Scale factor
1
50
)
c
A bicycle 120 cm high.
(Scale factor
1
)
2
d
A train 4 metres high.
(Scale factor
1
100
e
Mr Smith’s house 5 metres high.
(Scale factor
1
20
6.
)
).
Sir Francis has a model of his yacht on top of his
dining room table.
The scale of the model is 1 : 20.
If the length of his real yacht is 15 metres, what is
the length of his model ?
7.
The giraffe in this picture is
1
50
real life size.
If the actual giraffe is 4 metres tall, what will the
height of the giraffe in the picture be ?
8.
The scale of an ordinance survey map is 1 : 1000.
What would the length of a path be on a map,
if the real length of the path is 100 metres ?
9.
The two pictures shown below are rectangular.
reduced
? cm
12 cm
4 cm
32 cm
The smaller one is similar to the larger, but naturally it has been reduced in size.
a
Look at the length of the longer side in each rectangle and state by how much the
larger rectangle has been reduced. ( 41 , 12 , 51 .... ?)
b
Use this information to find the height of the smaller rectangle marked ? cm.
(Do not measure it)
National 4 Book N4-1
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Chapter 21 - Enlargement 2
10. These carpets are similar, but the second one is an enlargement of the first one.
2m
?m
3m
7·5 m
a
Write down the scale factor from the smaller carpet to the larger one.
(It is not a whole number).
b
Use this information to find the breadth of the larger carpet (marked ?).
11. These playing cards are similar.
a
b
Write down the scale factor from the
smaller card to the larger one.
Use this information to find the length
of the side of the card marked x cm.
x cm
6 cm
4 cm
6 cm
12. Mother flamingo has a daughter who is an exact replica of herself, but of course
is smaller.
90 cm
30 cm
Mum
Daughter
a
If mother’s height is 90 cm and daughter’s height is 30 cm, write down the
scale factor from mother to daughter.
b
Mum’s beak is 15 cm long. How long will the daughter’s beak be ?
National 4 Book N4-1
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Chapter 21 - Enlargement 2