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Measurement, NAP-K3-CA34

Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.

The length of the paddock is 2.8 kilometres.
 

 
How wide is the paddock?

Write your answer, in kilometres to one decimal place?

    kilometres
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`1.3`

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`text(Express as a perimeter equation:)`

`2 xx 2.8 + 2x` `= 8.2`
`2x` `= 2.6`
`:. x` `= 1.3\ text(km)`

Measurement, NAP-F3-CA32 SA

A square has an area of 169 square centimetres.

What is the perimeter?

   centimetres
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`52`

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`text(Let)\ \ x = text(length of 1 side)`

`text(Area) = x xx x` `= 169`
`x^2` `= 169`
`x` `= sqrt 169`
  `= 13\ text(cm)`

 

`:.\ text(Perimeter)` `= 4 xx 13`
  `= 52\ text(cm)`

Measurement, NAP-G3-NC29 SA

The length of this rectangle is one and a half times its height.
 

 
The perimeter of the rectangle is 40 centimetres.

What is the area of the rectangle?

  square centimetres
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`96\ text(cm²)`

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`text(Let)\ \ \ x` `=\ text(height)`
`3/2 x` `=\ text(length)`
`2 xx (x + 3/2 x)` `= 40`
`5x` `= 40`
`x` `= 8`
`:.\ text(Area)` `= x(3/2 x)`
  `= 8 xx 12`
  `= 96\ text(cm²)`