©2018 Compass Learning TechnologiesLive Mathematics on the Web →A4 Paper Folding

A4 Paper Folding

 

Fold a piece of A4 paper as shown. (Note that A4 paper is 29.7 x 21 cm)

Explore the relationship between the position of the fold (OP) and the area of the triangle formed.

When is this area greatest?

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  1. Drag the point P to find the height value for which the area of the triangle is greatest.

     

  2. Build an algebraic model for the area of the triangle by defining the following functions:

    height(x) =

     

    hypot(x) =

     

    base(x) =

     

    myarea(x) =

     

 

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  • Using Calculus build the derivative function for myarea(x) and use this to find the exact value of the height for which the area of the triangle is greatest:

    myderiv(x) =

     

    myderiv(x) = 0 when x =

     

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    Peter Fox and Steve Arnold. Created with GeoGebra


      

    This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!

    Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!

     

     

    And just wait until you try this with TI-nspire CAS!

     

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    ©2018 Compass Learning TechnologiesLive Mathematics on the Web ← GeoGebra Showcase