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**0 **

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**+1 **

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