Similarity, SMB-012

Poppy uses a photocopier to enlarge this picture.

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

By what factor is the area of the picture increased? (2 marks)

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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)`