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Similarity, SMB-027

 


 

  1. What scale factor is used to convert Circle A into Circle B.   (1 mark)

  2. Complete this equation:
  3.      Area of Circle A = _____ × Area of Circle B.  (1 mark)

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  1. \(\dfrac{1}{3}\)
  2. \(9\)
Show Worked Solution

i.     \(\text{Scale factor}\ = \dfrac{\text{Diameter B}}{\text{Diameter A}} = \dfrac{0.8}{2.4} = \dfrac{1}{3} \)
 

ii.     \(\text{Scale factor (B to A)} = \dfrac{\text{Diameter A}}{\text{Diameter B}} = \dfrac{2.4}{0.8} = 3 \)

\(\text{Scale factor (Area)} = 3^2 = 9 \)

\(\therefore\ \text{Area of Circle A = 9 × Area of Circle B} \)

Similarity, SMB-011

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?   (2 marks)

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`text(20 cm)`

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

 

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

Similarity, SMB-009

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 in centimetres, correct to 1 decimal place?    (2 marks)

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`1.1\ text(cm)`

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`text{Since 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`
  `=1.0666…`
  `=1.1\ text{cm  (1 d.p.)}`

Measurement, STD1 M5 2022 HSC 5 MC

Two similar figures are shown.
 

What is the value of `x` ?

  1. 6
  2. 8
  3. 18
  4. 27
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`C`

Show Worked Solution

`text{Scale factor}\ =3/2 =1.5`

`:.\ x = 1.5 xx 12 = 18`
  

`text{Alternate solution}`

`text{Using sides of similar figures in the same ratio:}`

`x/12` `=3/2`  
`x` `=12 xx (3/2)`  
`x` `=18`  

   
`=> C`

Measurement, STD2 M7 2007 HSC 4 MC

What scale factor has been used to transform Triangle `A` to Triangle `B`?
  

  1. `1/2`
  2. `3/4`
  3. `2`
  4. `3`
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`A`

Show Worked Solution

`text(Take two corresponding sides)`

`text(In)\ Delta A:\ 3\ text(cm)`

`text(In)\ Delta B:\ 1 \frac{1}{2}\ text(cm)`

`:.\ text(Scale factor converting)\ Delta A\ text(to)\ Delta B = frac{1}{2}`

`=>  A`

Measurement, STD2 M1 2013 HSC 17 MC

Triangles  `ABC`  and  `DEF`  are similar.
  

Which expression could be used to find the value of  `x`?

  1. `yxx10/15`
  2. `yxx10/23`
  3. `yxx15/10`
  4. `yxx23/15`
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 38%

`text(We know)\ \ Delta ABC\ text(|||)\ Delta DEF`

`:.\ (AB)/(AC)` `=y/10=(DE)/(DF)=x/15`
`x/15` `=y/10`
`x` `=yxx15/10`

 
`=> C`