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Geometry, NAP-K4-CA33 SA

Robin is designing a target with centre `O`.

The diameter of the smallest circle is 36 cm.
 

 
Robin makes  `AC = 1 1/4 xx AB`  and  `BC = 1/2 xx CD`.

What is the diameter of the whole target, `XD`?

     cm
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`90\ text(cm)`

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`OB = 1/2 xx 36 = 18`

`AC = 1 1/4 xx 36 = 45`

`BC = 45 – 36 = 9`

`CD = 2 xx 9 = 18`

 

`:.\ text(Diameter)\ XD`

`= 2 xx text(radius)`

`= 2 xx (18 + 9 + 18)`

`= 90\ text(cm)`

Filed Under: Ratio and Scale in Geometry, Ratio and Scale in Geometry Tagged With: Band 10, smc-3188-40-Similarity, smc-896-40-Similarity

Geometry, NAP-A4-CA25

A traffic light is 2.4 m tall. Its shadow from a nearby floodlight is 3 m long.
 

 
What is the height of the floodlight?

`text(3.6 m)` `text(3.8 m)` `text(4.0 m)` `text(4.2 m)`
 
 
 
 
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`text(4.0 m)`

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`text(Triangles are similar,)`

`text(S)text(ince similar triangles have sides in)`

`text(similar ratios:)`

`h/5` `= 2.4/3`
`:. h` `= (5 xx 2.4)/3`
  `= 4\ text(metres)`

Filed Under: Ratio and Scale in Geometry, Ratio and Scale in Geometry Tagged With: Band 9, smc-3188-40-Similarity, smc-896-40-Similarity

Geometry, NAP-F4-NC32 SA

Trapeziums `ABCD` and `AEFG` are similar.
 

What is the distance from `E` to `F`?

  metres
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`2\ text(m)`

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`text(S)text(ince trapeziums are similar,)`

`(EF)/(BC)` `= (AG)/(AD)`
`(EF)/8` `= 3/12`
`EF` `= (3 xx 8)/12`
  `= 2\ text(m)`

 

Filed Under: Ratio and Scale in Geometry, Ratio and Scale in Geometry Tagged With: Band 10, smc-3188-40-Similarity, smc-896-40-Similarity

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