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Sixteen metres of fencing are available to enclose a rectangular garden.

Represent the area of the garden as a function of the length of the one side.

What dimensions provide an area greater than 12m^2?

Micheala95  May 13, 2017
#1
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Sixteen metres of fencing are available to enclose a rectangular garden.

Represent the area of the garden as a function of the length of the one side.

$$A=l\times b\\b=\frac{z-2l}{2}\\b=\frac{14m-2l}{2}$$

$$A=f(l)=l\times (7m-l)=l\times 7m-l^2$$

$$A=f(l)=l\times 7m-l^2$$

!

asinus  May 14, 2017
#2
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Let  one side  =  x

The......the  other side  =   (16 - 2x) / 2  =  8 - x

And the  area, A(x),  can be represented  as

A ( x)  =  x ( 8 - x)   =     -x^2 + 8x

To  find  out  the dimensions that would make the area > 12 m^2   we have

-x^2 + 8x  > 12

Look  at  the graph, here : https://www.desmos.com/calculator/umwcrycnrg

It  shows  that  the area will be greater than 12m^2  when   2 m < x < 6 m

CPhill  May 14, 2017
edited by CPhill  May 14, 2017

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