smc-3188-20-Enlargement

Geometry, NAP-L4-CA13

Kransky has a photo which is 25 cm wide and 10 cm high

He wants to enlarge it to make a poster with a width of 50 cm.

What will be the height of the poster?

`text(20 cm)`	`text(25 cm)`	`text(75 cm)`	`text(125 cm)`

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`text(20 cm)`

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`text(Scale factor)`	`= text(new width)/text(old width)`
	`= 50/25`
	`= 2`

`:.\ text(New height)`	`= 2 xx 10`
	`= 20\ text(cm)`

Geometry, NAP-A4-NC08

The actual body length of a beetle Brad has caught is 24 mm.

A scale drawing of the beetle is shown below.

What scale is used in the drawing?

	1 cm represents 5 mm
	1 cm represents 2 mm
	2 cm represents 1 mm
	5 cm represents 1 mm

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`text(1 cm represents 2 mm)`

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`text(Scale:)`

`12\ text(cm)`	`: 24\ text(mm)`
`120\ text(mm)`	`: 24\ text(mm)`
`5`	`: 1`

`text(In the options given, the ratio of)\ 5 : 1\ text(occurs when)`

`1\ text(cm represents 2 mm)`

Geometry, NAP-A4-CA11

Poppy uses a photocopier to enlarge this picture.

The enlarged picture is 3 times as high and 3 times as wide as the original.

The area of the enlarged picture is

	3 times the area of the original.
	6 times the area of the original.
	9 times the area of the original.
	24 times the area of the original.

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`text(9 times the area of the original)`

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`text{Method 1}`

`text{Dimensions increased by a factor of 3}`

`:.\ text{Area increased by a factor of}\ 3^2 = 9`

`text{Method 2}`

`text(Area of original picture)\ = 3 xx 5 = 15\ text(cm)^2`

`text(Area of enlarged picture)\ = 9 xx 15 = 135\ text(cm)^2`

`:.\ text(Factor)\ = 135/15 = 9\ text(times)`

Geometry, NAP-C4-CA07

Juanita wanted to print a larger copy of her photo of a tree.

She increased the scale by a factor of 3.

She named the first picture Photo A and the second picture Photo B.

If Photo B is 3.2 cm high, how high is Photo A?

`0.8\ text(cm)`	`1.12\ text(cm)`	`1.07\ text(cm)`	`9.6\ text(cm)`

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`1.07\ text(cm)`

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`text(S)text(ince Photo B is increased by a factor of 3,)`

`text(Height of Photo B)/text(Height of Photo A)`	`=3`
`:.\ text(Height of Photo A)`	`=text(Height of Photo B)/3`
	`=3.2/3`
	`=1.07\ text(cm)`

Geometry, NAP-E4-CA29

A company logo is 14 cm by 9 cm.

Pablo wants to project it onto a screen that is 4.2 m by 3 m.

Pablo enlarges the logo as big as possible without distorting its proportions.

What are the dimensions of the enlarged logo, once projected, in cm?

cm by

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`420\ text(cm) xx 270\ text(cm)`

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`4.2\ text(m) = 420\ text(cm)`

`text(Magnification) = 420/14 = 30\ text(times).`

`text(Check if height fits on a 30 times enlargement:)`

`30 xx 9\ text(cm) = 270\ text{cm (which fits)}`

`:.\ text(Dimensions are:)\ \ 420\ text(cm) xx 270\ text(cm)`